Trigonometric Functions Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
If sin⁡θ=35\sin\theta = \frac{3}{5} and θ\theta is in Quadrant II, find cos⁡θ\cos\theta and tan⁡θ\tan\theta.

Solution

  1. 1
    Use sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1: cos⁡2θ=1−925=1625\cos^2\theta = 1 - \frac{9}{25} = \frac{16}{25}, so cos⁡θ=±45\cos\theta = \pm\frac{4}{5}.
  2. 2
    In Quadrant II, cosine is negative: cos⁡θ=−45\cos\theta = -\frac{4}{5}.
  3. 3
    tan⁡θ=sin⁡θcos⁡θ=3/5−4/5=−34\tan\theta = \frac{\sin\theta}{\cos\theta} = \frac{3/5}{-4/5} = -\frac{3}{4}.

Answer

cos⁡θ=−45,tan⁡θ=−34\cos\theta = -\frac{4}{5}, \quad \tan\theta = -\frac{3}{4}
The Pythagorean identity sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1 lets you find one trig function from another. The quadrant determines the sign.

About Trigonometric Functions

Trigonometric functions (sin, cos, tan, etc.) relate angles in right triangles to side ratios and extend to periodic functions of real numbers via the unit circle.

Learn more about Trigonometric Functions →

More Trigonometric Functions Examples

Example 1 easy

Evaluate [formula] and [formula].

Example 2 medium

Find the exact value of [formula].

Example 3 easy

Evaluate [formula].

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