Find arcsin [cos (Pi/2)]
The answer is 0.
How do you solve this problem? Thanks.
You have to use the definition of cos and sin. If you use the geometric definition using a right triangle, then you see that
cos(x) = sin(pi/2-x)
If you take the cosine of one angle (alpha), you get the same as when you take the sin of the other angle (beta). Now, alpha is 90° - beta, so the result follows.
So, arcsin[cos(pi/2)] =
arcsin[sin(0)] = 0
You are standing 35 feet from a billboard. The angle of elevation is 58 degrees. How tall is the billboard? Round your answer to the nearest foot
To solve the problem, follow these steps:
1. Start by finding the cosine of π/2: cos(π/2) = 0. This is because the cosine of π/2 is equal to 0 according to the unit circle.
2. Next, find the arcsine of 0. The arcsine function is the inverse of the sine function. Since sin(0) = 0, the arcsine of 0 is also 0.
Therefore, the answer to arcsin[cos(π/2)] is 0.
To solve this problem, you need to have an understanding of trigonometric functions and their inverses.
The given expression is arcsin [cos (π/2)]. Let's break it down step by step:
1. Start with the inner part of the expression, which is cos(π/2).
- The value of cos(π/2) is 0.
- This is because the cosine function evaluates to 0 at π/2 (90 degrees), where the unit circle intersects the x-axis.
2. Now, you have arcsin [0].
- The arcsin function is the inverse of the sine function.
- The arcsin function returns the angle (in radians or degrees) whose sine is equal to the given value.
- The sine function evaluates to 0 at 0 radians (0 degrees) and also at π radians (180 degrees), and then repeats every 2π radians (360 degrees).
3. Since the arcsin function is an inverse of the sine function, the arcsin of 0 is 0.
- Therefore, the answer to the given expression arcsin [cos (π/2)] is 0.
In summary, the solution to arcsin [cos (π/2)] is 0.