Trigo: Obtuse Angle
In this lesson, you will learn how to work with obtuse angles in trigonometry. An obtuse angle is any angle greater than 90° but less than 180°. To handle these angles, we use the concept of a related acute angle (also called the reference angle). For sine, the value remains positive, but for cosine and tangent, the values become negative.
By rewriting the obtuse angle in terms of its reference (acute) angle, you can apply the standard trigonometric ratios.
Related Lessons:
The Three Obtuse Angle Formula
Given an obtuse angle A, we can “convert” sine, cosine and tangent of the obtuse angle A into an acute (reference) angle. Note that the sum of the obtuse angle A and the acute (reference) angle is always 180°.
The three formulae are:
- \(sin{A}=+sin{(}180^\circ-A)\)
- \(cos{A}=-cos{(}180^\circ-A)\)
- \(tan{A}=-tan{(}180^\circ-A)\)
Example
Given the diagram above, we are going to convert the sine, cosine and tangent of the obtuse angle ADC into the reference acute angle ADB.