Trigonometry - Sin, Cos, Tan

What is the value of ?

$\frac{\sqrt3+1}{2}$

$\frac{\sqrt3-1}{2}$

Explanation

Solve each term separately.

$cos(30)= \frac{\sqrt3}{2}$

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

Add both terms.

$\frac{\sqrt3}{2}+\frac{1}{2}= \frac{\sqrt3+1}{2}$

Which of the following describes the ratio of sine?

$\frac{\text{opposite}}{\text{hypotenuse}}$

${}\frac{\text{opposite}}{\text{adjacent}}$

${}\frac{\text{adjacent}}{\text{hypotenuse}}$

$\frac{\text{adjacent}}{\text{opposite}}$

$\frac{\text{hypotenuse}}{\text{adjacent}}$

Explanation

Sine is by definition of sides in a right triangle is opposite side over hypotenuse.

To remember this, use SOH CAH TOA.

SOH: Sine=Opposite/Hypotenuse

CAH: Cosine=Adjacent/Hypotenuse

TOA: Tangent=Opposite/Adjacent

Calculate $tan(\frac{4\pi}{3})$ .

$\sqrt{3}$

$-\sqrt{3}$

Explanation

The tangent function has a period of $\pi$ units. That is,

$tan(x+n\pi)=tanx$

for all $n\in\mathbb{Z}$ .

Since $\frac{4\pi}{3}=\frac{\pi}{3}+\pi$ , we can rewrite the original expression $tan(\frac{4\pi}{3})$ as follows:

$tan(\frac{4\pi}{3})=tan(\frac{\pi}{3}+\pi)$

$=tan(\frac{\pi}{3})$

$=\frac{sin(\frac{\pi}{3})}{cos(\frac{\pi}{3})}$

$=\frac{(\frac{\sqrt{3}}{2})}{(\frac{1}{2})}$

$=\sqrt{3}$

Hence,

$tan(\frac{4\pi}{3})=\sqrt{3}$

Round to the nearest hundredth.

Use your calculator to find:

$\cos \frac{3\pi}{8}$

None of the above

Explanation

Before plugging the function into the calculator make sure the mode of the calculator is set to radians,

plug in

$\cos \frac{3\pi}{8}$

which is equal to .

$\left ( \sin15 + \cos\15 \right )^{2}$ What is the closest value to this expression?

Explanation

First you have to know the equation for $\left ( a+b\right )^{2} = a^{2}+2ab+b^{2}$ and apply it to our equation. Second the formula of $\sin^{2}+\cos^{2}=1$ will allow you to get rid of the square sin and cos. Third the equation $\sin2x = 2\sin \cos$ will allow you to get rid of the . Therefore, we will have a $\sin(30)$ , and that will be equal to . Sum and and you will get