Unit 2 Analytic Trigonometry Assignment Sheet
Lesson
Verifying Trig
Identities
Extra Problems
Verify each identity
1. sin 𝑥 sec 𝑥 = tan 𝑥
6.
2. tan(− 𝑥) cos 𝑥 = −sin 𝑥
7. sin2 𝑥 (1 + cot 2 𝑥) = 1
3. sec 𝑥 − sec 𝑥 sin2 𝑥 = cos 𝑥
8. sin 𝑥 tan 𝑥 =
tan 𝑥 cot 𝑥
csc 𝑥
4. cos 2 𝑥 − sin2 𝑥 = 1 − 2 sin2 𝑥 9.
5. csc 𝑥 − sin 𝑥 = cot 𝑥 cos 𝑥
Sum and
Difference
Formulas
tan2 𝑥
sec 𝑥
10.
= sin 𝑥
1−cos2 𝑥
cos 𝑥
Learning Targets
-I can use Pythagorean,
Reciprocal, Quotient
and Even-Odd
Identities.
-I can verify
trigonometric identiies.
= sec 𝑥 − cos 𝑥
1−cos 𝑥
sin 𝑥
= csc 𝑥 − cot 𝑥
Use a sum or difference formula to find the exact value.
1. sin 105°
2. cos 75°
3. tan 15°
-I can use sum and
difference formulas to
find exact values of trig
functions.
Write each expression as the sine, cosine, or tangent of an
angle, then find the exact value.
5. sin 25° cos 5° + cos 25° sin 5°
-I can use sum and
difference formulas to
verify trigonometric
identities
6. cos 75° cos 15° − sin 75° sin 15°
Verify each identity.
𝜋
7. sin (𝑥 + 2 ) = cos 𝑥
Double Angle
and Half
Angle
Formulas
Use the information given to find the exact value of
𝒔𝒊𝒏 𝟐𝜽, 𝒄𝒐𝒔 𝟐𝜽, 𝒂𝒏𝒅 𝒕𝒂𝒏 𝟐𝜽.
1. cos 𝜃 = 24/25 , 𝜃 𝑖𝑠 𝑖𝑛 𝑞𝑢𝑎𝑑𝑟𝑎𝑛𝑡 𝐼𝑉.
2. cot 𝜃 = 2 , 𝜃 𝑖𝑠 𝑖𝑛 𝑞𝑢𝑎𝑑𝑟𝑎𝑛𝑡 𝐼𝐼𝐼.
3. sin 𝜃 = −9/41 , 𝜃 𝑖𝑠 𝑖𝑛 𝑞𝑢𝑎𝑑𝑟𝑎𝑛𝑡 𝐼𝐼𝐼.
-I can use double-angle
and half-angle formulas
to find exact values of
trigonometric
functions.
Write each expression as the sine, cosine, or tangent of an
angle, then find the exact value.
4. 2sin 15° cos 15°
5. cos 2 75° − sin2 75°
Use a half-angle formula to find the exact value.
6. sin 15°
7. cos 157.5°
7𝜋
8. tan 8
-I can use double-angle
and half-angle formulas
to verify trig identities
Inverse Trig
Functions
Solving Trig
Equations
Find the exact value.
1
1. sin−1
2
−1 √2
2. sin
2
1
−1
3. sin (− 2)
√3
4. cos −1 2
√2
5. cos −1 (− 2 )
−1
6. cos
0
7. tan−1
√3
3
−1
8. tan (−√3)
𝜋
3
9. sin−1 (𝑠𝑖𝑛 )
2𝜋
)
3
5𝜋
11. sin−1 (𝑠𝑖𝑛 6 )
10. cos−1 (𝑐𝑜𝑠
Find all solutions of each equation.
1. 2 cos x + √3 = 0
5. 5 sin x + 1 = 3 sin x
2. sin² Ɵ - 1 = 0
3. 4 cos² x -1 = 2
4. sin² x + 2 sin x – 3 = 0
-I can graph inverse
trigonometric
functions.
-I can use inverse
trigonometric functions
to find an angle.
-I can use inverse
trigonometric functions
to find the exact value
of the trigonometric
function.
-I can solve
trigonometric
equations, using
inverse functions and
the graphing calculator.
These learning targets are to help guide you during this unit. It is up to you to
keep track of your learning. The assignments in the middle are for if you feel you
need extra practice. As always, if you need any extra help, please don’t hesitate
to ask me. I’m available most mornings. Please email me to let me know you’re
coming.