Using exact values,find the value of:
(A=30degrees)
sin 2A + tan 3A/2 - cos A + sec(A+15), when A= 30degrees
There were no parentheses and no exponents. please help by showing the work in details. Thank you!
I pluged in the numbers and got this
I don't know if its right or wrong..
2*1/2 + (3*sqrt3/3)/2 -sqrt3/2 + (2sqrt3+15)
Your answer is incorrect. For A = 30 degrees, it is easy to give exact values for each term
sin60 + tan45 -cos30 +sec(45)
= (sqrt3)/2 +1 -(sqrt3)/2 +sqrt2
= 1 + sqrt2
Thank you soo much.
Can you add 1 to the sqrt of 2 .
Or was that the final answer.
That was the final and exact answer.
To find the value of the expression, we need to evaluate each trigonometric function using the given angle A = 30 degrees and then substitute those values into the expression.
Let's break down the expression step by step:
1. sin 2A:
Using the double-angle identity, sin 2A = 2 * sin A * cos A.
Substituting A = 30 degrees, we have:
sin 2A = 2 * sin 30 * cos 30.
Now, we know that sin 30 degrees = 1/2 and cos 30 degrees = sqrt(3)/2, so we can substitute those values:
sin 2A = 2 * (1/2) * (sqrt(3)/2) = sqrt(3)/2.
2. tan 3A/2:
Using the half-angle identity, tan (A/2) = (1 - cos A) / sin A.
Let's calculate tan (3A/2), substituting A = 30 degrees:
tan (3A/2) = tan (3 * 30/2) = tan 45 degrees.
Since tan 45 degrees = 1, we can substitute this value into the expression:
tan 3A/2 = 1.
3. -cos A:
Substituting A = 30 degrees, we have:
-cos A = -cos 30 = -sqrt(3)/2.
4. sec(A + 15):
Using the definition of secant, sec A = 1 / cos A.
So, sec (A + 15) = 1 / cos (A + 15).
Substituting A = 30 degrees, we have:
sec (A + 15) = 1 / cos (30 + 15) = 1 / cos 45 degrees.
Since cos 45 degrees = sqrt(2)/2, we can substitute this value into the expression:
sec (A + 15) = 1 / (sqrt(2)/2) = 2 / sqrt(2) = sqrt(2).
Now, let's substitute all the values back into the original expression:
sin 2A + tan 3A/2 - cos A + sec(A + 15)
= sqrt(3)/2 + 1 - sqrt(3)/2 + sqrt(2)
= sqrt(3)/2 - sqrt(3)/2 + sqrt(2) + 1
= sqrt(2) + 1
Therefore, the value of the expression when A = 30 degrees is sqrt(2) + 1.