Evaluate (sin45 degrees)(cos30 degrees) / sec45 degrees
a)5
b)7/3
c)1/2
d)7/2
My best guess is 1/2 but I'm not sure if I did the problem right. I found sin 45 and cos 30 multiplied the vvalues together and then divided them by sec45. My answer was 0.5303295 and I rounded that off to 1/2.
Please help.
I gave the wrong answers!
The correct answers are
a)1/4
b)sqrt3/4
c)sqrt3/2
d)sqrt3
Now 1/2 isn't even an option so now I know I did it wrong.
Put (sin45 degrees)(cos30 degrees) / sec(45 degrees)
into the Google search engine. That elminates a, d, c...all of those have to be greater than one.
To evaluate the expression (sin45 degrees)(cos30 degrees) / sec45 degrees, let's break it down step by step.
1. Firstly, we need to find the values for sin45 degrees, cos30 degrees, and sec45 degrees.
- To find sin45 degrees, you can use the special right triangle. In a 45-45-90 triangle, the sides are in the ratio 1:1:sqrt(2). So, sin45 degrees is equal to 1 / sqrt(2).
- To find cos30 degrees, you can use the special right triangle again. In a 30-60-90 triangle, the sides are in the ratio 1:sqrt(3):2. So, cos30 degrees is equal to sqrt(3) / 2.
- To find sec45 degrees, we can use the reciprocal relationship between secant and cosine. Sec45 degrees is the reciprocal of cos45 degrees. Since cos45 degrees is 1 / sqrt(2), sec45 degrees is sqrt(2) / 1, which simplifies to sqrt(2).
2. Now, substitute the values we found into the original expression:
(sin45 degrees)(cos30 degrees) / sec45 degrees
= [(1 / sqrt(2))(sqrt(3) / 2)] / sqrt(2)
= (sqrt(3) / (sqrt(2) * 2)) / sqrt(2)
= sqrt(3) / (sqrt(2) * 2) * (1 / sqrt(2))
= (sqrt(3) * 1) / (sqrt(2) * 2 * sqrt(2))
= sqrt(3) / (2 * 2)
= sqrt(3) / 4
So, the correct answer is a) 1/4.