Find a if a is between 0 degrees and 180 degrees, and:

a. Sin a = cos a
b. sin^2 = 3/4
c. tan^2 = 1/3

I have no clue on where to start any help would be much appreciated.

sina = cosa

divide by cosa and you have
tana = 1
a = 45

sin^2 = 3/4
sina = ±√3/2
a = 60,120

tan^2 = 1/3
tana = ±1/√3
a = 30,150

Looks like you need to review your "standard" angles where the values are well known, and the various signs in the quadrants.

yeah ive just recently learnt about the unit circle and all that other stuff but thanks

To find the values of angle a that satisfy the given trigonometric equations, let's go through each equation step by step:

a. Sin a = cos a:

Since we are given that a is between 0 degrees and 180 degrees, we can use the fact that sin(a) = cos(90 - a) for this range.

So, we have:
Sin a = cos a
=> Sin a = sin(90 - a)

In order for Sin a to be equal to sin(90 - a), angle a needs to be equal to (90 - a).

Therefore:
a = 90 - a

Let's solve for a:
2a = 90
a = 90 / 2
a = 45 degrees

So, the solution to equation (a) is a = 45 degrees.

b. sin^2 a = 3/4:

To solve this equation, we can take the square root of both sides:
sin a = √(3/4)

Now, we need to find the values of a that satisfy this equation. However, there is no exact value for the square root of (3/4) because it is an irrational number. We can approximate it as follows:

sin a ≈ √(0.75)

Using a scientific calculator or trigonometric tables, we can find the inverse sine (sin^(-1)) of √(0.75). This will give us the angles whose sine is approximately equal to √(0.75).

Using a calculator, sin^(-1)(√(0.75)) ≈ 48.19 degrees.

So, the solutions to equation (b) are a ≈ 48.19 degrees and (180 - 48.19) ≈ 131.81 degrees.

c. tan^2 a = 1/3:

To solve this equation, we can take the square root of both sides:
tan a = √(1/3)

Now, we need to find the values of a that satisfy this equation. Similarly to equation (b), there is no exact value for the square root of (1/3) as it is irrational. We can approximate it as follows:

tan a ≈ √(0.33)

Using a calculator, tan^(-1)(√(0.33)) ≈ 18.43 degrees.

So, the solutions to equation (c) are a ≈ 18.43 degrees and (180 + 18.43) ≈ 198.43 degrees.

In summary, the solutions for the given trigonometric equations are:
a. a = 45 degrees
b. a ≈ 48.19 degrees and a ≈ 131.81 degrees
c. a ≈ 18.43 degrees and a ≈ 198.43 degrees.