Download Teacher Notes – KEY CRS FUN 703

CW#69H: Trig of All Angles
Honors Geometry
Teacher Notes – KEY
CRS
FUN 703 - Exhibit knowledge of unit circle trigonometry.
Objective
10.15B - Evaluate the 6 trigonometric functions of any angle using reference angles.
Review:
If  is not a quadrantal angle, the sign of a trig function depends on the quadrant in which  lies:
Draw Picture:
*A way for students to remember is
the saying:


“A Smart Trig Class” or “All Students
Take Calculus”
ASTC
*All positive in Q1
*Sine (and reciprocal function
cosecant) positive in Q2
*Tangent (and reciprocal cotangent)
positive in Q3
*Cosine (and reciprocal secant)
positive in Q4
Example 1: If tan  0 and cos  0, name the quadrant in which  lies.
Unit circle w/ radius r


*y will always be the side opposite
*x will always be the side adjacent
*the hypotenuse is the radius, r

Ex 2. Let (8, -10) be a point on the terminal side of an angle 
in standard position. Find the exact value of each of the six trig
functions of  .

CW#69H: Trig of All Angles
Honors Geometry
Classroom Copy –DO NOT WRITE ON!
CRS
FUN 703 - Exhibit knowledge of unit circle trigonometry.
Objective
10.15B - Evaluate the 6 trigonometric functions of any angle using reference angles.
Directions: A point on the terminal side of an angle θ is given. Find the exact value of sec, csc, and cot.
1. (-3,4)
2. (5,-12)
3. (2, -3)
4. (-1, -2)
5. (-3,-3)
6. (2, -2)
Directions: Use reference angles to find the exact value of each expression. WATCH YOUR SIGNS!
7. sin 510⁰
8. cos 600⁰
9. cot 330⁰
10. sin
3
4
11. tan (7π)
12. csc 300⁰
13. Find the exact value: do NOT use a
calculator.
14. Find the exact value:
cos 540⁰  tan (  405⁰)
sin 270ᵒ + cos(-180ᵒ)
15. Find the exact value:
16. Find the exact value:
tan π + sin π
6cos (

3
) + 2tan (  )
4
3
17. Review: Find the three smallest positive
angles coterminal to -800°.
18. Review: Find the three smallest positive
angles coterminal to 6413°.
19. Review: Given the following triangle, find
the remaining sides.
20. Review: Given the following triangle, find
the missing angles and side.
26
r
10
y
M
40ᵒ
x
33
Q