Luxury/Triganometry with Annicka: How do we solve Linear Trigonometric Equations?

Question: How do we solve Linear Trigonometric Equations?

Linear Trignometric equations will look like this:Find all angles, 0≤A<360, that satisfy the equation below, to the nearest 10th of a degree.

So for the equation: 3TanA-7= TanA-8

In order to sole Linear Trig equations as shown above follow these steps.

Step 1: Substitute the tri function(TanA) with a variable of x to make solving easier:

3 x - 7

=

x - 8

Step 2: Now solve like a regular equation, bringing the constant(7) to the right side:

Step 3: Now divide by the coefficient(2) of x:

$2 x 2$	$=$	$- 1 2$
$x$	$=$	$- 1 2$

Step 4: Now plug in the trig function back in for x:

tan A

=

- 1 2

Step 5: Now determine the quadrants were TanA is negative in order to find the reference angle:(All-Students-Take-Calculus)

Tan is negative in quadrants II and IV

In order to find the reference angle we need to plug in the -1/2 using the invere of tan as shown below

tan−1(12)=26.57≈26.6∘
Step 6: Plug in the reference angle of 26.6 as shown below:

Quads: II, IV Ref: 26.6 \circ

A II = 180 - 26.6 = 153.4 \circ

A IV = 360 - 26.6 = 333.4 \circ

TRY IT YOURSELF:
Find all angles, 0≤A<360, that satisfy the equation below, to the nearest 10th of a degree.

9 sin B - 2

=

sin B - 8

x - 8