Question

If sin(θ−π/2) = −0.47, find cos(−θ).
a) 0.47
b) -0.47
c) 0.87
d) -0.87

Answer 1

I think it’s A, let me know if I’m wrong or not

Answer 2

To find cos(-θ), we can use the identity cos(-θ) = cos(θ). Given sin(θ−π/2) = -0.47, we can find sin(θ) and substitute it into the identity to find cos(-θ). Thus, the answer is: a) 0.47

Step-by-step explanation:

To find cos(-θ), we can use the identity cos(-θ) = cos(θ). Since we are given that sin(θ−π/2) = -0.47, we can use this to find sin(θ). Subtracting π/2 from both sides of the equation gives us θ = arcsin(-0.47) + π/2. Then, substituting this value of θ into the identity for cos(-θ), we get cos(-θ) = cos(arcsin(-0.47) + π/2). Finally, we can use a calculator to find the approximate value of cos(-θ).

To find cos(-θ) given that sin(θ−π/2) = −0.47, we'll first use trigonometric identities to relate sin(θ−π/2) to cos(θ). The identity we'll use is: sin(α − π/2) = −cos(α) From this identity, if we replace α with θ: sin(θ − π/2) = −cos(θ) We know from the question that sin(θ−π/2) is −0.47: −cos(θ) = −0.47

We can remove the negatives from both sides to get: cos(θ) = 0.47 Now, let's use another identity that deals with the cosine of a negative angle: cos(−θ) = cos(θ) Therefore, cos(−θ) is equal to cos(θ), which we found is 0.47. Thus, the answer is: a) 0.47