Hi, can someone please teach me how to solve this?
Find the exact value of the trigonometric expression
cos(89)sin(29)+sin(89)sin(29)
recall that
cos(a-b) = cos(a)cos(b) + sin(a)sin(b)
So, after fixing your typo, you have cos(89-29) = cos(60) = 1/2
Thank You Steve. I now understand it :)
Sure! To find the exact value of the trigonometric expression, let's break it down into smaller parts.
First, let's consider the expression cos(89)sin(29). To evaluate this, we need to find the cosine of 89 degrees and the sine of 29 degrees.
Step 1: Convert the angle measurements to radians.
To find the values of trigonometric functions, we usually work with radians rather than degrees. We can convert degrees to radians by multiplying by π/180.
89 degrees = (89 * π/180) radians
29 degrees = (29 * π/180) radians
Step 2: Evaluate the trigonometric functions.
cos(89 * π/180) = cos(π/2) = 0
sin(29 * π/180) = sin(29π/180) ≈ 0.4833
So, cos(89)sin(29) equals 0.
Next, let's consider the expression sin(89)sin(29). Again, we need to find the sine values of 89 degrees and 29 degrees.
sin(89 * π/180) = sin(π/2) = 1
sin(29 * π/180) = sin(29π/180) ≈ 0.4833
So, sin(89)sin(29) is approximately equal to 0.4833.
Now, let's add the two results together:
0 + 0.4833 ≈ 0.4833
Therefore, the exact value of the trigonometric expression cos(89)sin(29) + sin(89)sin(29) is approximately 0.4833.