Trigonometry

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Questions 1 - 10

How many radians are in $270^\circ$ ?

$\frac{3\pi}{2}$

$2\pi$

$\pi$

$\frac{2\pi}{3}$

$\frac{5\pi}{2}$

Explanation

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{270^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$270^\circ*\pi=180^\circ*x$

Isolate :

$\frac{270^\circ}{180^\circ}\pi=x$

$\frac{3\pi}{2}=x$

If Angle equals $72^{\circ}$ , what is the equivalent angle in radians (to the nearest hundredth)?

$1.26\ radians$

$4125.29\ radians$

$4.125\ radians$

$1256.6\ radians$

$0.628\ radians$

Explanation

To convert between radians and degrees, it is important to remember that:

$\pi, rad = 180^{\circ}$

With this relationship in mind, we can convert from degrees to radians with the following formula:

$72^{\circ}\cdot \frac{\pi}{180^{\circ}} = 1.26,rad$

If Angle equals $72^{\circ}$ , what is the equivalent angle in radians (to the nearest hundredth)?

$1.26\ radians$

$4125.29\ radians$

$4.125\ radians$

$1256.6\ radians$

$0.628\ radians$

Explanation

To convert between radians and degrees, it is important to remember that:

$\pi, rad = 180^{\circ}$

With this relationship in mind, we can convert from degrees to radians with the following formula:

$72^{\circ}\cdot \frac{\pi}{180^{\circ}} = 1.26,rad$

How many radians are in $270^\circ$ ?

$\frac{3\pi}{2}$

$2\pi$

$\pi$

$\frac{2\pi}{3}$

$\frac{5\pi}{2}$

Explanation

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{270^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$270^\circ*\pi=180^\circ*x$

Isolate :

$\frac{270^\circ}{180^\circ}\pi=x$

$\frac{3\pi}{2}=x$

What angle is complementary to $34^\circ$ ?

$56^\circ$

$66^\circ$

$34^\circ$

$146^\circ$

$156^\circ$

Explanation

Two complementary angles add up to $90^\circ$ .

Therefore, $34^\circ+x^\circ=90^\circ$ .

$x^\circ=90^\circ-34^\circ$

$x^\circ=56^\circ$

Trig_id

What is $\theta$ if and ?

$51.34^{\circ}$

$53.14^{\circ}$

$55.14^{\circ}$

$0.90^{\circ}$

$89.60^{\circ}$

Explanation

In order to find $\theta$ we need to utilize the given information in the problem. We are given the opposite and adjacent sides. We can then, by definition, find the $\tan$ of $\theta$ and its measure in degrees by utilizing the $\arctan$ function.

$\tan=\frac{opposite}{adjacent}$

$\tan=\frac{10}{8}$

$\tan=1.25$

Now to find the measure of the angle using the $\arctan$ function.

$\theta=\arctan1.25$

$\rightarrow 51.34^{\circ}$

If you calculated the angle's measure to be $0.90^{\circ}}$ then your calculator was set to radians and needs to be set on degrees.

What angle is complementary to $34^\circ$ ?

$56^\circ$

$66^\circ$

$34^\circ$

$146^\circ$

$156^\circ$

Explanation

Two complementary angles add up to $90^\circ$ .

Therefore, $34^\circ+x^\circ=90^\circ$ .

$x^\circ=90^\circ-34^\circ$

$x^\circ=56^\circ$

Which of these is equal to $\frac{\text{hypotenuse}}{\text{adjacent}}$ for angle ?

$\sec{x}$

$\csc{x}$

$\sin x$

$\cot{x}$

$\cos{x}$

Explanation

$\sec{x}=\frac{\text{hypotenuse}}{\text{adjacent}}$ , as it is the inverse of the $\cos{x}$ function. This is therefore the answer.

Which of these is equal to $\frac{\text{hypotenuse}}{\text{adjacent}}$ for angle ?

$\sec{x}$

$\csc{x}$

$\sin x$

$\cot{x}$

$\cos{x}$

Explanation

$\sec{x}=\frac{\text{hypotenuse}}{\text{adjacent}}$ , as it is the inverse of the $\cos{x}$ function. This is therefore the answer.

Trig_id

What is $\theta$ if and ?

$51.34^{\circ}$

$53.14^{\circ}$

$55.14^{\circ}$

$0.90^{\circ}$

$89.60^{\circ}$

Explanation

$\tan=\frac{opposite}{adjacent}$

$\tan=\frac{10}{8}$

$\tan=1.25$

Now to find the measure of the angle using the $\arctan$ function.

$\theta=\arctan1.25$

$\rightarrow 51.34^{\circ}$

If you calculated the angle's measure to be $0.90^{\circ}}$ then your calculator was set to radians and needs to be set on degrees.

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