 # Trig Ratios in all Four Quadrants (4)

In this worksheet, students work out trigonometric functions by looking at the quadrants in which the angles lie. Key stage:  KS 4

Curriculum topic:  Ratio, Proportion and Rates of Change

Curriculum subtopic:  Compare Lengths, Areas and Volumes Using Ratio Notation/Scale Factors

Difficulty level:   ### QUESTION 1 of 10

In this worksheet, you will work with trigonometric functions of any angle using the ASTC circle to determine in which quadrants the functions are positive, before finding "equivalent" trig ratios of angles less than 90º.

Remember that angles are measured anticlockwise from the 0º line.

The following diagram shows the angle 200º on the ASTC circle. Notice that the 200º line makes an angle of 20º with the horizontal.

We always look at the horizontal.

This shows that:

tan 200º = tan 20º as tan is positive in this 3rd quadrant.

sin 200º = - sin 20º as sin is negative in this 3rd quadrant.

cos 200º = -cos 20º as cos is negative in this 3rd quadrant.

Example

If cos 15º = 0.966, calculate

cos 525º

Answer

On the ASTC circle, 525º makes an angle of 15º with the horizontal. The only trig ratio that is positive in this quadrant is sin, which means that cos is negative in this quadrant.

cos 525º = cos 165º = - cos 15º = -0.966

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of sin 170º

0.174

-0.174

0.985

-0.985

0.176

-0.176

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of tan 170º

0.174

-0.174

0.985

-0.985

0.176

-0.176

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of sin 190º

0.174

-0.174

0.985

-0.985

0.176

-0.176

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of cos 190º

0.174

-0.174

0.985

-0.985

0.176

-0.176

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of tan 350º

0.174

-0.174

0.985

-0.985

0.176

-0.176

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of cos 350º

0.174

-0.174

0.985

-0.985

0.176

-0.176

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of cos 370º

0.174

-0.174

0.985

-0.985

0.176

-0.176

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of tan 370º

0.174

-0.174

0.985

-0.985

0.176

-0.176

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of sin 550º

0.174

-0.174

0.985

-0.985

0.176

-0.176

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of cos 710º

0.174

-0.174

0.985

-0.985

0.176

-0.176

• Question 1

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of sin 170º

CORRECT ANSWER
0.174
EDDIE SAYS
The 170° line makes an angle of 10° with the horizontal.
170° is in the 2nd quadrant where sin is positive.
• Question 2

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of tan 170º

CORRECT ANSWER
-0.176
EDDIE SAYS
The 170° line makes an angle of 10° with the horizontal.
170° is in the 2nd quadrant where tan is negative.
• Question 3

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of sin 190º

CORRECT ANSWER
-0.174
EDDIE SAYS
The 190° line makes an angle of 10° with the horizontal.
190° is in the 3rd quadrant where sin is negative.
• Question 4

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of cos 190º

CORRECT ANSWER
-0.985
EDDIE SAYS
The 190° line makes an angle of 10° with the horizontal.
190° is in the 3rd quadrant where cos is negative.
• Question 5

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of tan 350º

CORRECT ANSWER
-0.176
EDDIE SAYS
The 350° line makes an angle of 10° with the horizontal.
350° is in the 4th quadrant where tan is negative.
• Question 6

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of cos 350º

CORRECT ANSWER
0.985
EDDIE SAYS
The 350° line makes an angle of 10° with the horizontal.
350° is in the 4th quadrant where cos is positive.
• Question 7

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of cos 370º

CORRECT ANSWER
0.985
EDDIE SAYS
The 370° line makes an angle of 10° with the horizontal.
370° is in the 1st quadrant where cos is positive.
• Question 8

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of tan 370º

CORRECT ANSWER
0.176
EDDIE SAYS
The 370° line makes an angle of 10° with the horizontal.
370° is in the 1st quadrant where tan is positive.
• Question 9

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of sin 550º

CORRECT ANSWER
-0.174
EDDIE SAYS
The 550° line makes an angle of 10° with the horizontal.
550° - 360° = 190° which is in the 3rd quadrant where sin is negative.
• Question 10

You are given that:

sin 10º = 0.174

cos 10º = 0.985

tan 10º = 0.176

State the value of cos 710º

CORRECT ANSWER
0.985
EDDIE SAYS
The 710° line makes an angle of 10° with the horizontal.
710° - 360° = 350° which is in the 4th quadrant where cos is positive.
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