Lesson 4.3

Trigonometric Functions on the Unit Circle

Lesson Overview:

Unit Circle

Steps for finding the exact value of trig function of angle with degrees

Steps for finding the exact value of trig function of angle with Radians

The Unit Circle

Steps:

Look at the angle given and determine if it is between 0-360 degrees
Draw the picture
Fill in the lengths of the legs and the hypotenuse
Find the sine, cosine, and tangent of the angle based off of the unit circle.
Use the three major trigonometric functions to determine the three minor trigonometric functions.

Steps:

Look at the angle given and determine if it is between 0-2π
Draw the picture
Fill in the lengths of the legs and the hypotenuse.
Find the sine, cosine, and tangent of the angle based off of the unit circle.
Use the three major trigonometric functions to determine the three minor trigonometric functions.

Real World Application

If the angle of elevation to the top of a tree is 65°. How far are you away from the tree, if the tree's height is 27 feet? Round your answer to the nearest tenth

Step 1: Draw and label a picture for this world problem.

Step 2:

Now, set up your trig ratio and solve for a side length.

tan(65) = opposite/adjacent

tan(65) = 27/d

d= 27/tan(65)

d=12.6 feet

SAT Prep Problem

If Sin(A)=0.5 and side BC=10, find the length of the hypotenuse, AB.

Answer:

To set up this problem, we first need to think back to the definition of our trig functions. If you recall, the sine of an angle in a right triangle is defined as the opposite side over the hypotenuse, or Sin A = o/h
Given that Sin(A)=0.5, we can combine our two equations into Sin A = o/h = 0.5
And with the knowledge that the side opposite of A has a length of 10, our equation now becomes 10/h = 0.5
Moving h over gives us 10 = 0.5h
And finally solving gives us h=20
So our final answer is the hypotenuse, length AB, is 20 units long.

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