Given angle x,where 0 <= x <= 360 (degrees) solve for to the nearest degree.

a)cos(2x) = 0.6420
b)sin(x + 20) = 0.2045
c)tan(90 - 2x) = 1.6443

How did you get 2x=211 ?

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To solve each of these trigonometric equations, we will need to make use of inverse trigonometric functions and the unit circle. Let's solve each equation step by step:

a) cos(2x) = 0.6420:
We can start by applying the inverse cosine function (also known as arccos) to both sides of the equation. This will give us:
2x = arccos(0.6420)

To find the value of arccos(0.6420), you can use a calculator. The result is approximately 49.77 degrees.

Now, we want to solve for x, so we divide both sides of the equation by 2:
x = 49.77 / 2
x ≈ 24.89

Therefore, the nearest degree value for x is 25 degrees.

b) sin(x + 20) = 0.2045:
To solve this equation, we'll start by subtracting 20 from both sides of the equation:
x + 20 = arcsin(0.2045)

Using a calculator to find the value of arcsin(0.2045), we get approximately 11.79 degrees.

Now, we subtract 20 from both sides to isolate x:
x = 11.79 - 20
x ≈ -8.21

Therefore, the nearest degree value for x is -8 degrees.

c) tan(90 - 2x) = 1.6443:
First, we'll solve for the expression inside the tangent function by subtracting 90 from both sides:
90 - 2x = arctan(1.6443)

Using a calculator to find the value of arctan(1.6443), we get approximately 57.75 degrees.

Now, we subtract 90 from both sides to isolate -2x:
-2x = 57.75 - 90
-2x ≈ -32.25

Finally, we divide both sides by -2 to solve for x:
x ≈ -32.25 / -2
x ≈ 16.13

Therefore, the nearest degree value for x is 16 degrees.

Remember to always use a calculator for the inverse trigonometric functions' calculations, as they are usually not easy to determine manually.

just use your calculator to find the angle with the given property. Then solve for x.

For example, tan 58.7° = 1.6443
Since the period of tan(x) is 180°, you have to find x where

90-2x = 58.7: 2x = 31.3, so x = 16
2x = 211, so x = 106
also, continuing on, x = 196,286

Do the others in like wise.