Unit Circle

What is the length of the hypotenuse of the triangle? (Think about it as a radius)

OP= (a)  

Label OP on your paper.

Using θ as a reference angle, mark the triangle sides as Opp, Adj, and Hyp.

Label these on the triangle on your paper.

Now, use the given triangle to represent $$\sin\theta$$ and $$\cos\theta$$ in terms of the variables given in the diagram.

What about tangent? Use the triangle to answer the following questions.

In terms of x and y, what does tanθ equal?

tanθ=​ ​ (a)  

In terms of sinθ and cosθ, what does tanθ equal?

tanθ=​ (b)  

Look at YOUR unit circle. What is the reference angle for $$\frac{4\pi}{3}$$ ?

Reference angle = ​ (a)  

Look at YOUR unit circle. What is the reference angle for $$\frac{7\pi}{4}$$ ?

Reference angle = ​ ​ (a)  

Unlike right triangle trigonometry, sine and cosine may be negative.

Thinking about how sine, cosine, and tangent relate to (x,y) coordinate pairs on the unit circle, find the quadrants where:

sine is positive: ​ (a)   ​& (b)  

sine is negative: ​ ​ (c)   &​ (d)  

Unlike right triangle trigonometry, sine and cosine may be negative.

Thinking about how sine, cosine, and tangent relate to (x,y) coordinate pairs on the unit circle, find the quadrants where:

cosine is positive: ​ (a)   ​& (b)  

cosine is negative: ​ ​ (c)   &​ (d)  

Unlike right triangle trigonometry, sine and cosine may be negative.

Thinking about how sine, cosine, and tangent relate to (x,y) coordinate pairs on the unit circle, find the quadrants where:

tangent is positive: ​ (a)   ​& (b)  

tangent is negative: ​ ​ (c)   &​ (d)   ​

Find the exact value of the following trig expressions.

Try to remember these results without looking at the unit circle.

$$\sin\left(\frac{\pi}{3}\right)=$$ ​ (a)  

$$\sin\left(\frac{7\pi}{6}\right)=$$ ​ ​ ​ (b)  

$$\cos\left(\frac{5\pi}{4}\right)=$$ ​ (c)  

$$\cos\left(-\frac{\pi}{3}\right)=$$ ​ (d)