# How do I solve the equation 90 cos X - 14 sin X = 72?

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90, 14 and 72 are parameters as well, but those are results from another equation.

90, 14 and 72 are parameters as well, but those are results from another equation.

##### 2 Answers

Write

#### Explanation:

You can write the 14

Upon squaring on both sides and solving the quadratic in

#### Explanation:

90cos x - 14sin x = 72

Divide both sides by 90

Call

The equation (1) becomes:

Reminder: cos a.cos b - sin a.sin b = cos (a + b)

Therefor,

a. x + t = 37.81 -->

b. x + 8.84 = - 37.81 -->

For general answers, add

Check by calculator:

x = - 46.61 --> 90cos x = 61.83 --> 14sin x = - 10.17

90cos x - 14sin x = 61.83 + 10.17 = 72.00. Proved.