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## Using Sine and Cosine

#### Trigonometry - HSG-SRT.D.10

How to use Sine and Cosine - Trigonometry is the branch of mathematics that deals with the measurements and the relationships between the side lengths and the angles of a triangle. When we are dealing with right-angled triangles, we use the following trigonometric functions for are calculations; sin Β = Opposite/Hypotenuse, cos Β = Adjacent/Hypotenuse, tan Β = Opposite/Adjacent And their inverses, given by; csc ⁡ Β =(Hypotenuse )/Opposite, sec ⁡Β =Hypotenuse/Adjacent, cot ⁡Β =Adjacent/Opposite However, when we are dealing with other types of triangles, such as isosceles, scalene, and equilateral, these six trigonometric functions are not used. It is where the sine and the cosine rule enter trigonometry. Sine Rule - The sine rule is given by; a/sin⁡A =b/sin⁡B =c/sin⁡C There are two conditions when you can use the sine rule; When two angles and one side is given. When two sides and one non-included angle is given, it is sometimes called the ambiguous case. Cosine Rule - The cosine rule is given by; a2=b2+c2 - 2bc cos⁡Α b2=a2 + c2- 2ac cos⁡Β c2=a2 + b2 - 2ab cosμ There are two conditions when you can use the cosine rule; When two sides and one included angle is given. All three sides are given. A series of printable worksheets that help students learn to use these functions as tools to help reveal information about right triangles.

### Printable Worksheets And Lessons

• Missing Sides Step-by-step Lesson -We get familiar with our favorite triangle theorems, once again.

• Guided Lesson - I tried to touch on all the major applications of these problems that appear on standardized tests. See how I did.

• Guided Lesson Explanation - I used a slight smaller font here to reduce the number of pages that you need to print.

• Practice Worksheet - A series of solid pages for you to work on here.

• Matching Worksheet - Match the parts of the theorems to help this one make more sense and finish the problems faster.  #### Homework Sheets

We hit every part of a triangle with this one.

• Homework 1 - The law of sin is based on the proportionality of side and angle in triangle. The law states that for the angle of a non right angle, each angle of the triangle has the same ratio of angle measure to sine value.
• Homework 2 - We have to write down the givens. Use the law of cosines, substitute, and simplify. Isolate cos A find the inverse.
• Homework 3 - We have to write down what is known. Alternative forms of law of cosines can be substituted.

#### Practice Worksheets

We give you 2 angles and 1 side of a triangle, you tell us the rest.

• Practice 1 - Use the Law of Sine and the Law of Cosine to find the missing sides and angles of each triangle. BC = 14, A = 30°, and B = 90°
• Practice 2 - Find the value of < P, < L, and < A.
• Practice 3 - Substitute the known value into the law of Sine to find the missing lengths.

#### Math Skill Quizzes

Find all the missing sides and measures.

• Quiz 1 - The law of sine is based on the proportionality of the side and angle in a triangle.
• Quiz 2 - Find that missing value.
• Quiz 3 - Figure out which function best fits your need here.