## Trigonometric Function Applications

 6.6 Trigonometric Function Applications

• Steps to solve a trigonometric equation:

 1 Simplify the equation by using suitable identities if needed. 2 Determine the reference angle, and use the value of the trigonometric ratio without taking into consideration the signs. 3 Find the angles in the quadrants that correspond to the signs of the trigonometric ratio and range. 4 Write the solutions obtained.

• Solving trigonometric equations

 Example Solve the equation  $$\text{sin }\theta = -0.5446$$ for $$0^{\circ} \leqslant \theta \leqslant 360^{\circ}$$. Solution: \begin{aligned} \text{Reference angle, } \alpha &= \text{sin}^{-1}(0.5446)\\ \alpha &= 33^{\circ} \end{aligned} $$\text{sin }\theta$$ is negative, so $$\theta$$ is in the quadrant III and IV for $$0^{\circ} \leqslant \theta \leqslant 360^{\circ}$$. \begin{aligned} \theta &= 180^{\circ} + 33^{\circ} \text{ and }360^{\circ} - 33^{\circ}\\ &=213^{\circ} \text{ and } 327^{\circ} \end{aligned}

• The knowledge of trigonometric functions is often used to solve problems in our daily lives as well as in problems involving trigonometry