Right Triangle Trigonometry

Integrated Math 4

Mrs. Tyrpak

Definitions: Let be an acute angle of a right triangle, then

Hypotenuse

𝜃Opposite

Adjacent

Example #1

Find the exact value of the six trig functions of theta.

4

3

Example #2

Find the exact value of sin(45), cos(45), and tan(45).

Example #3

Use an equilateral triangle to find the exact values of sin(60), cos(60), sin(30), cos(30).

Special Angles

sin(30)= cos(30)= tan(30)=

sin(45)= cos(45)= tan(45)=

sin(60)= cos(60)= tan(60)=

Co-functions of complementary angles are equal

sin(90 – x)= cosx cos(90 -x) = sinx

tan(90 – x)= cotx cot(90 -x) = tanx

sec(90 – x)= cscx csc(90-x) = secx

Applications of Right Triangles

Angle of elevation: the angle from the horizontal UPWARD to the object

Angle of depression: the angle from the horizontal DOWNWARD to the object

Example #4

A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5 degrees. How tall is the tree?

Example #5

From a 60-foot observation tower on the coast, a Coast Guard officer sights a boat in difficulty. The angle of depression of the boat is 4.5 degrees. How far is the boat from the shoreline?

Reciprocal Identities

Reasoning with Reciprocal Functions

Sketch a right triangle with . Evaluate the remaining 5 trigonometric functions.

Reasoning with Reciprocal Functions

Sketch two angles such that

Find the remaining functions for both angles.

Thanks for your hard work!

Don’t forget to complete both the extension and enrichment assignments

before you move on.

Remember to take a short break if you feel stuck. It will help clear your head

and help you focus!