assume A= alpha
using complementary rule how do I solve for alpha?
cos(2A+40) =sin(3A-60)
I don't understand how to start the question. What are the steps in solving for alpha.
Do i get cos to equal sin somehow?
for the complementary angle property
sinA = cos(90-A)
so
cos(2A+40) = sin(3A-60)
sin(90 - (2A+40) ) = sin(3A-60)
sin(50-2A) = sin(3A-60)
then
50-2A = 3A-60
110 = 5A
A = 22°
To solve for alpha (A) using the complementary rule, you need to convert the given equation involving cosine (cos) and sine (sin) into their complementary functions. The complementary rule states that:
cos(90° - θ) = sin(θ)
sin(90° - θ) = cos(θ)
Now, let's solve the equation step by step:
Step 1: Identify the angles involving A on each side of the equation:
Left side: 2A + 40
Right side: 3A - 60
Step 2: Convert the given equation using the complementary rule:
cos(90° - (2A + 40)) = sin(3A - 60)
Step 3: Simplify the angles inside the functions:
cos(90° - 2A - 40) = sin(3A - 60)
Step 4: Apply the complementary rule to each side:
sin(2A + 40) = sin(3A - 60)
Step 5: Now, since the sine function is equal on both sides, you can equate the angles inside the sine functions:
2A + 40 = 3A - 60
Step 6: Solve for A:
Combine like terms: 2A + 40 = 3A - 60
Rearrange the equation: 3A - 2A = 40 + 60
Simplify: A = 100
Therefore, the value of alpha (A) is 100°.