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Cogito

Trigonometry · Chapter 1 · Lesson 2

Practice Worksheet

The Reciprocal Ratios

Three more names for ratios you already know.

12 problems · about 20 minutes · G-SRT.C.8, F-TF.C.8

NameDate

Figure — use these to answer the problems

Set the legs, read the three ratios, then flip each one in your head.

sin — opposite over hypotenuse0.60
cos — adjacent over hypotenuse0.80
tan — opposite over adjacent0.75
The marked angle36.87°

Adjacent leg4

Opposite leg3

Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

1
Which ratio is the reciprocal of cosine?
- Secant.
- Cosecant.
cos θ = 0.5. What is sec θ?
Answer
cos θ = 0.25. What is sec θ?
Answer
tan θ = 4. What is cot θ, as a decimal?
Answer
sin θ = 0.2. What is csc θ?
Answer

Build It Up

The same ideas with more to keep track of.

3 problems

Opposite 3, hypotenuse 5. What is csc θ, as a decimal to two places?
Answer
What is sec 0°?
Answer
cot θ = 1. What is tan θ?
Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

9
Which of these are undefined?
- csc 0°
- cot 0°
- sec 0°
- sin 0°
- Tick every box that applies.
Adjacent 8, opposite 6. What is cot θ, as a decimal to two places?
Answer
The Flip
sin θ = 0.5. What is csc θ?
Answer
12
The Pairs
Match each ratio with its reciprocal.
Draw a line from each item on the left to its match on the right.
- sine
- cosine
- tangent
- cosecant
- secant
- cotangent