Sec, Csc, Ctan - Trigonometry

Card 1 of 32

0

Didn't Know

0

Didn't Know

Knew It

0

1 of 2019 left

Question

Find the value of the trigonometric function in fraction form for triangle .

What is the secant of $\angle A$ ?

Tap to reveal answer

Answer

The value of the secant of an angle is the value of the hypotenuse over the adjacent.

Therefore:

$sec \angle A = $\frac{hypotenuse}{adjacent}$ = $\frac{25}{24}$$

← Didn't Know|Knew It →

Question

Which of the following is the equivalent to $\frac{1}{\csc\theta}$ ?

Tap to reveal answer

Answer

Since $\csc\theta=\frac{1}{\sin\theta}$$ :

$$\frac{1}{\csc\theta}$=\frac{1}{\frac{1}${\sin\theta}}=1*$\frac{\sin\theta}{1}$=\sin\theta$

← Didn't Know|Knew It →

Question

For the above triangle, what is $\sec (\theta)$ if , and ?

Tap to reveal answer

Answer

Secant is the reciprocal of cosine.

$\sec \left ( \theta\right ) = $\frac{1}{\cos\left( \theta\right)}$$

It's formula is:

$\sec(\theta) = $\frac{\textup{hypotenuse}$}{\textup{adjacent}}$

Substituting the values from the problem we get,

$\sec(\theta) = $\frac{17}{15}$ = 1.13$

← Didn't Know|Knew It →

Question

For the above triangle, what is $\cot (\theta)$ if , and ?

Tap to reveal answer

Answer

Cotangent is the reciprocal of tangent.

$\cot \left ( \theta\right ) = $\frac{1}{\tan\left( \theta\right)}$$

It's formula is:

$\cot(\theta) = $\frac{\textup{adjacent}$}{\textup{opposite}}$

Substituting the values from the problem we get,

$\cot(\theta) = $\frac{24}{18}$ = 1.33$

← Didn't Know|Knew It →

Question

Evaluate:

Tap to reveal answer

Answer

Evaluate each term separately.

$sec(60)= $\frac{1}{cos(60)}$=\frac{1}{0.5}$= 2$

$csc(45)= $\frac{1}{sin(45)}$= $\frac{1}{\frac{\sqrt2}${2}}= $\frac{2}{\sqrt2}$\times$\frac{\sqrt2}{\sqrt2}$= $\frac{2\sqrt2}{2}$=\sqrt2$

$sec(60)-csc(45)=2-$\frac{2\sqrt2}{2}$=2-\sqrt2$

← Didn't Know|Knew It →

Question

Determine the value of $cot($\frac{\pi}{4}$)$ .

Tap to reveal answer

Answer

Rewrite $cot($\frac{\pi}{4}$)$ in terms of sine and cosine.

$cot($\frac{\pi}{4}$)= $\frac{cos(\frac{\pi}{4}$)}{sin($\frac{\pi}{4}$)}=\frac{\frac{\sqrt2}{2}$}{$\frac{\sqrt2}{2}$}=1$

← Didn't Know|Knew It →

Question

Pick the ratio of side lengths that would give sec C.

Tap to reveal answer

Answer

$\sec\theta=\frac{1}{\cos\theta }$$

Find the ratio of Cosine and take the reciprocal.

$\cos\theta=\frac{AC}{CB}$\rightarrow \sec\theta=\frac{1}{\frac{AC}${CB}}=\mathbf{$\frac{CB}{AC}$}$

← Didn't Know|Knew It →

Question

If $\sin x=\frac{28}{53}$$ , $\cot x=$

Tap to reveal answer

Answer

The sine of an angle in a right triangle (that is not the right angle) can be found by dividing the length of the side opposite the angle by the length of the hypotenuse of the triangle.

From this, the length of the side opposite the angle is proportional to 28, and the length of the hypotenuse is proportional to 53.

Without loss of generality, we'll assume that the sides are actually of length 28 and 53, respectively.

We'll use the Pythagorean theorem to determine the length of the adjacent side, which we'll refer to as .

$\begin{align} $y&=$\sqrt{53^2$$-28^2$}$\ &=$\sqrt{2809-784}$\ &=$\sqrt{2025}$\ &=45 \end{align}$

The cotangent of an angle in a right triangle (that is not the right angle) is can be found by dividing the length of the adjacent side by the length of the opposite side.

$\cot x=\frac{45}{28}$$

← Didn't Know|Knew It →

Question

Find the value of the trigonometric function in fraction form for triangle .

What is the secant of $\angle A$ ?

Tap to reveal answer

Answer

The value of the secant of an angle is the value of the hypotenuse over the adjacent.

Therefore:

$sec \angle A = $\frac{hypotenuse}{adjacent}$ = $\frac{25}{24}$$

← Didn't Know|Knew It →

Question

Which of the following is the equivalent to $\frac{1}{\csc\theta}$ ?

Tap to reveal answer

Answer

Since $\csc\theta=\frac{1}{\sin\theta}$$ :

$$\frac{1}{\csc\theta}$=\frac{1}{\frac{1}${\sin\theta}}=1*$\frac{\sin\theta}{1}$=\sin\theta$

← Didn't Know|Knew It →

Question

For the above triangle, what is $\sec (\theta)$ if , and ?

Tap to reveal answer

Answer

Secant is the reciprocal of cosine.

$\sec \left ( \theta\right ) = $\frac{1}{\cos\left( \theta\right)}$$

It's formula is:

$\sec(\theta) = $\frac{\textup{hypotenuse}$}{\textup{adjacent}}$

Substituting the values from the problem we get,

$\sec(\theta) = $\frac{17}{15}$ = 1.13$

← Didn't Know|Knew It →

Question

For the above triangle, what is $\cot (\theta)$ if , and ?

Tap to reveal answer

Answer

Cotangent is the reciprocal of tangent.

$\cot \left ( \theta\right ) = $\frac{1}{\tan\left( \theta\right)}$$

It's formula is:

$\cot(\theta) = $\frac{\textup{adjacent}$}{\textup{opposite}}$

Substituting the values from the problem we get,

$\cot(\theta) = $\frac{24}{18}$ = 1.33$

← Didn't Know|Knew It →

Question

Evaluate:

Tap to reveal answer

Answer

Evaluate each term separately.

$sec(60)= $\frac{1}{cos(60)}$=\frac{1}{0.5}$= 2$

$csc(45)= $\frac{1}{sin(45)}$= $\frac{1}{\frac{\sqrt2}${2}}= $\frac{2}{\sqrt2}$\times$\frac{\sqrt2}{\sqrt2}$= $\frac{2\sqrt2}{2}$=\sqrt2$

$sec(60)-csc(45)=2-$\frac{2\sqrt2}{2}$=2-\sqrt2$

← Didn't Know|Knew It →

Question

Determine the value of $cot($\frac{\pi}{4}$)$ .

Tap to reveal answer

Answer

Rewrite $cot($\frac{\pi}{4}$)$ in terms of sine and cosine.

$cot($\frac{\pi}{4}$)= $\frac{cos(\frac{\pi}{4}$)}{sin($\frac{\pi}{4}$)}=\frac{\frac{\sqrt2}{2}$}{$\frac{\sqrt2}{2}$}=1$

← Didn't Know|Knew It →

Question

Pick the ratio of side lengths that would give sec C.

Tap to reveal answer

Answer

$\sec\theta=\frac{1}{\cos\theta }$$

Find the ratio of Cosine and take the reciprocal.

$\cos\theta=\frac{AC}{CB}$\rightarrow \sec\theta=\frac{1}{\frac{AC}${CB}}=\mathbf{$\frac{CB}{AC}$}$

← Didn't Know|Knew It →

Question

If $\sin x=\frac{28}{53}$$ , $\cot x=$

Tap to reveal answer

Answer

The sine of an angle in a right triangle (that is not the right angle) can be found by dividing the length of the side opposite the angle by the length of the hypotenuse of the triangle.

From this, the length of the side opposite the angle is proportional to 28, and the length of the hypotenuse is proportional to 53.

Without loss of generality, we'll assume that the sides are actually of length 28 and 53, respectively.

We'll use the Pythagorean theorem to determine the length of the adjacent side, which we'll refer to as .

$\begin{align} $y&=$\sqrt{53^2$$-28^2$}$\ &=$\sqrt{2809-784}$\ &=$\sqrt{2025}$\ &=45 \end{align}$

The cotangent of an angle in a right triangle (that is not the right angle) is can be found by dividing the length of the adjacent side by the length of the opposite side.

$\cot x=\frac{45}{28}$$

← Didn't Know|Knew It →

Question

Find the value of the trigonometric function in fraction form for triangle .

What is the secant of $\angle A$ ?

Tap to reveal answer

Answer

The value of the secant of an angle is the value of the hypotenuse over the adjacent.

Therefore:

$sec \angle A = $\frac{hypotenuse}{adjacent}$ = $\frac{25}{24}$$

← Didn't Know|Knew It →

Question

Which of the following is the equivalent to $\frac{1}{\csc\theta}$ ?

Tap to reveal answer

Answer

Since $\csc\theta=\frac{1}{\sin\theta}$$ :

$$\frac{1}{\csc\theta}$=\frac{1}{\frac{1}${\sin\theta}}=1*$\frac{\sin\theta}{1}$=\sin\theta$

← Didn't Know|Knew It →

Question

For the above triangle, what is $\sec (\theta)$ if , and ?

Tap to reveal answer

Answer

Secant is the reciprocal of cosine.

$\sec \left ( \theta\right ) = $\frac{1}{\cos\left( \theta\right)}$$

It's formula is:

$\sec(\theta) = $\frac{\textup{hypotenuse}$}{\textup{adjacent}}$

Substituting the values from the problem we get,

$\sec(\theta) = $\frac{17}{15}$ = 1.13$

← Didn't Know|Knew It →

Question

For the above triangle, what is $\cot (\theta)$ if , and ?

Tap to reveal answer

Answer

Cotangent is the reciprocal of tangent.

$\cot \left ( \theta\right ) = $\frac{1}{\tan\left( \theta\right)}$$

It's formula is:

$\cot(\theta) = $\frac{\textup{adjacent}$}{\textup{opposite}}$

Substituting the values from the problem we get,

$\cot(\theta) = $\frac{24}{18}$ = 1.33$

← Didn't Know|Knew It →

0

Knew It