Cogito
Integrated Math 2 · Chapter 5 · Lesson 1
The Three Trigonometric Ratios
Similarity gives every right triangle a fingerprint.
12 problems · about 21 minutes · G-SRT.C.6, G-SRT.C.7
What this lesson teaches
The student defines sine, cosine and tangent and computes them from a right triangle.
- The acute angle alone determines the side ratios, because such triangles are all similar.
- Sine is opposite over hypotenuse, cosine adjacent over hypotenuse, tangent opposite over adjacent.
- Sine and cosine are always below 1.
Warm Up
Straightforward practice. Get the method working first.
5 problemsAdjacent 12, hypotenuse 13. Cosine to two decimal places?
Answer 0.92
Why About 0.92.
Why does one angle determine the ratios?
Answer All right triangles with that angle are similar.
Why Similarity forces the ratios to match.
Adjacent 4, hypotenuse 5. Cosine as a decimal?
Answer 0.8
Why 4 ÷ 5.
Opposite 8, hypotenuse 10. Sine as a decimal?
Answer 0.8
Why 8 ÷ 10.
Legs 6 and 8. What is the hypotenuse?
Answer 10
Why √(36 + 64).
Build It Up
The same ideas with more to keep track of.
3 problemsOpposite 6, adjacent 8. Tangent as a decimal?
Answer 0.75
Why 6 ÷ 8.
Can a sine ever exceed 1? 1 yes, 0 no.
Answer 0
Why The hypotenuse is longest.
Legs 5 and 12. What is the hypotenuse?
Answer 13
Why √169.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsMatch each ratio with its definition.
Answer Sine → Opposite over hypotenuse; Cosine → Adjacent over hypotenuse; Tangent → Opposite over adjacent
Why Only one of them leaves the hypotenuse out.
Opposite 5, hypotenuse 13. Sine to two decimal places?
Answer 0.38
Why 5 ÷ 13.
The Sine: Opposite 3, hypotenuse 5. What is the sine, as a decimal?
Answer 0.6
Why 0.6.
The Tangent: Opposite 3, adjacent 4. What is the tangent, as a decimal?
Answer 0.75
Why 0.75.