Trigonometry Equations

In this course on trigonometry equations, we will be looking at how to solve trigonometry equations of the form sine = d , cosine = d , tangent where d is a constant. Solving trigonometry equations is not difficult . Let us take you step by step on how to solve them and give examples of solving trigonometry equations.

Steps to solving trigonometry equations

1)Look at the sign of d (±) and find the possible quadrants that lies.

2)Calculate the basic angle, , which is always acute (between and )

3)Find all the values of in the required interval of angles.

Always remember that is measured from the positive x-axis.


Find all the values of for the trigonometry equation , where

trigonometry equation to solve, where

We refer to the ‘ASTC' diagram.

implies that is in the 3 rd or 4 th quadrant.

For the basic angle ,

and so


With this basic angle, we are able to calculate the values

of ? in the 3 rd and 4 th quadrant.

= ,

Below is another example to reinforce our concept of solving trigonometry equations.

b)Find all the possible values of x between and which satisfy the trigonometry equation

is in the 2 nd or 3 rd quadrant as indicated by the ‘ASTC' diagram.

For the basic angle ,

(correct to 1 decimal place)


For angle in this interval,

'Try it Yourself' Sections

Try solving these trigonometry equations yourself.

a) cosine = -0.3 where

b) tangent ( ) = -0.1 where

Return to Trigonometry Help or Basic Trigonometry .