Transcript Trigonometric Ratios

Warm-Up 1
Find the value of x.
Warm-Up 1
Find the value of x.
Trigonometric Ratios I
Objectives:
1. To discover the three main trigonometric
ratios
2. To use trig ratios to find the lengths of
sides of right triangles
Summary

A
side adjacent Θ
B
side opposite Θ
C
sin  opposite
hypotenuse
cos  adjacent
hypotenuse
tan  opposite
adjacent
SohCahToa
Soh
sin  opposite
hypotenuse
Cah
cos  adjacent
hypotenuse
Toa
tan  opposite
adjacent
Example 3
Find the values of the six trig ratios for α and
β.
Activity: Trig Table
Step 5: Finally, let’s check your values with
those from the calculator.
For sin, cos, and tan
1. Make sure your calculator is set to DEGREE in the
MODE menu.
2. Use one of the 3 trig keys. Get in the habit of
closing the parenthesis.
Example 4
To the nearest meter,
find the height of a
right triangle if one
acute angle
measures 35° and
the adjacent side
measures 24 m.
Example 5
To the nearest foot, find the length of the
hypotenuse of a right triangle if one of the
acute angles measures 20° and the
opposite side measures 410 feet.
Example 6
Use a special right triangle to find the exact
values of sin(45°) and cos(45°).
Example 7
Find the area of a
regular octagon
with a side length
of 6 inches.
Example 8
Find the value of x to the nearest tenth.
1. x =
2. x =
3. x =
Find the values of 𝑤 and 𝑥
Challenge Problem
• Make a conjecture about how the sine and
cosine of 30° angle are related.
Challenge Problem
• Make a conjecture about how the sine and
cosine of 60° angle are related.
Challenge Problem
• Square ABCD in the diagram at the right has side length
of 1, and midpoints of its sides are labeled P, Q, R, and
S. Find the length of a side of the shaded square