COSINE

Cosine

Definition Of Cosine

In a right-angles triangle Cosine is the ratio of length of the adjacent side to the length of the hypotenuse.

More About Cosine

Cosine is also written as cos.

Example of Cosine

EXAMPLE OF Cosine

cos θ = EXAMPLE OF Cosine & cos θ = 4/5

Video Examples: Sine and Cosine Rule 1 (GCSE Higher Maths)

Solved Example on Cosine

Ques: If x = 8 units, y = 15 units, and a = 17 units, then find the value of cos C in the right triangle ABC.

example of Cosine

Choices:

A. 15/17
B. 17/18
C. 17/15
D. 8/17
Correct Answer: D

Solution:

Step 1: Cos C = example of Cosine
Step 2: In â–³ABC, the adjacent side of C is and the hypotenuse is .
Step 3: So, Cos C =
Step 4: = 8/17 [Substitute BC = 8 and AC = 17.]

Quick Summary

Cosine is the ratio of the adjacent side to the hypotenuse in a right triangle.
Cosine is abbreviated as cos.

\[ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \]

🍎 Teacher Insights

Use visual aids and real-world examples to illustrate the concept. Emphasize the importance of correctly identifying the adjacent and hypotenuse sides. Use the mnemonic SOH-CAH-TOA.

🎓 Prerequisites

Right Triangles
Pythagorean Theorem
Basic Ratios

Check Your Knowledge

Q1: In a right triangle with adjacent side = 4 and hypotenuse = 5, what is the cosine of the angle?

3/5 4/5 3/4 5/4

Q2: If cos(θ) = 0, what is the value of θ in degrees (0 ≤ θ ≤ 90)?

0 30 45 90

Frequently Asked Questions

Q: What is the range of cosine values?
A: The range of cosine values is between -1 and 1, inclusive.

Q: How does cosine relate to the unit circle?
A: On the unit circle, the cosine of an angle is represented by the x-coordinate of the point on the circle.