1. Suppose we know sin a = and 0 < a < , and suppose we also know cos 3 = 2√³ and - < 3 < 0. Use this to find the exact values (not decimal approximations) for each of the following, showing all work in 3 your process, and illustrating each on a unit circle: a. sin(a + 3) b. cos(a + B) c. tan(a-3) (Hint for this one: Use the definition of tangent and the related formulas for sine and cosine, then simplify.) d. sin(2a) e. cos(28) f. cos() 8. sin (
1. Suppose we know sin a = and 0 < a < , and suppose we also know cos 3 = 2√³ and - < 3 < 0. Use this to find the exact values (not decimal approximations) for each of the following, showing all work in 3 your process, and illustrating each on a unit circle: a. sin(a + 3) b. cos(a + B) c. tan(a-3) (Hint for this one: Use the definition of tangent and the related formulas for sine and cosine, then simplify.) d. sin(2a) e. cos(28) f. cos() 8. sin (
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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d. sin (2 alpha)
e. sin (2 beta)
f. cos (alpha/2)
Transcribed Image Text:Prompts for Week 7 Collaborative Written Assignment A
1. Suppose we know sin a = and 0 < a < 1, and suppose we also know cos 3 = 2√5 and - < 3 < 0. Use this to find the exact values (not decimal approximations) for each of the following, showing all work in
your process, and illustrating each on a unit circle:
a. sin(a + 3)
b. cos(a + B)
c. tan(a 3) (Hint for this one: Use the definition of tangent and the related formulas for sine and cosine, then simplify.)
d. sin(2a)
e. cos(2/3)
f. cos (2)
g. sin (2)
2. Prove each of the following using identities, showing all work in the process.
a. cos(x+3)+sin(x) = 0
b. cos(x) sin(x) = cos(2x)
1+sin(2x)
C.
1+ secx x CSC x
sin(2x)
3. Find sin() using each of the following methods:
a. Write
as a sum of special angles and use an appropriate identity.
b. Write
as a difference of special angles and use an appropriate identity.
c. Write
as a half-angle and use an appropriate identity.
4. Write the function f (a) = sin(3a) -√3 cos(3a) using a single sine function and use the result to find the zeros of f (a) in [0, 27). Be sure to show all steps in your process.
5. Solve 2 sin(20) = 3 sin for solutions 0 = [0, 2π).
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