# Trigonometry with Oblique Triangles

## Cosine Law

To use the sine laws introduced last section, we need to know at least one complete side length to angle ratio including another known side length or angle. Sometimes we may not have that information, but instead you’re given all three side lengths and no angle. In this case, we…

## Sine Law

Thus far, we’ve learned how to efficiently solve right triangles using trigonometric functions. Remember that to “solve” a triangle means we’re finding all its unknown lengths and angles. What if we have a triangle that is not a right-angle triangle (called an oblique triangle)? If your oblique triangle has the following configurations:…

## Special Triangles

The angles shown below appear so frequently in problems that it is convenient to be able to write their trigonometric functions from memory. These angles are derived from these two triangles: If you’d like watch two examples where we use special triangles to find unknown angles, watch Question 1 in…

## Trigonometric Functions of Any Angle

The CAST rule you learned in the previous lesson suggests that for every ratio you evaluate using an inverse trigonometric function, there are at least two angles between 0° and 360° that represent that ratio. For example, if we’re given cos θ = 0.3345, using cos-1(0.3345) = θ we get 70.6°.…

## CAST Rule and Reference Angles

Given the right triangle shown below, a summary of all the trigonometric functions we’ve learned so far are listed: Trigonometric Functions: null Reciprocal Trigonometric Functions: null Inverse Trigonometric Functions: null Inverse Reciprocal Trigonometric Functions: null In the last unit, we explored all six of these trigonometric functions using angles found…