 # Trig Ratios in all Four Quadrants (3)

In this worksheet, students match 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

Select the trigonometric functions which are equal to one another.

sin 165º, -sin 65º, sin 15º, sin 525º, -sin 15º

On the ASTC circle, both 165º and 525º make an angle of 15º with the horizontal. The only trig ratio that is positive in this quadrant is sin.

sin 525º = sin 165º = sin 15º

Select all the trigonometric ratios which are equal to one another.

sin 10°

sin 190°

sin 170°

sin 530°

sin 80°

Select all the trigonometric ratios which are equal to one another.

sin 80°

sin 190°

-sin 10°

sin 110°

sin 550°

Select all the trigonometric ratios which are equal to one another.

cos 80°

cos 190°

-cos 10°

cos 110°

cos 550°

Select all the trigonometric ratios which are equal to one another.

tan 10°

tan 190°

-tan 10°

tan 110°

tan 550°

Select all the trigonometric ratios which are equal to one another.

tan 20°

tan 70°

-tan 70°

tan 110°

tan 470°

Select all the trigonometric ratios which are equal to one another.

sin 135°

sin 45°

-sin 45°

sin 505°

sin 495°

Select all the trigonometric ratios which are equal to one another.

cos 35°

-cos 35°

-cos 55°

cos 325°

cos 685°

Select all the trigonometric ratios which are equal to one another.

cos 245°

-cos 65°

cos 65°

cos -115°

cos 605°

Select all the trigonometric ratios which are equal to one another.

tan 55°

tan 245°

-tan 55°

tan 125°

tan 845°

Select all the trigonometric ratios which are equal to one another.

sin 222°

sin -138°

-sin 42°

sin 42°

-sin 48°

• Question 1

Select all the trigonometric ratios which are equal to one another.

sin 10°
sin 170°
sin 530°
EDDIE SAYS
The 170° line makes an angle of 10° with the horizontal.
170° is in the 2nd quadrant where sin is positive.
170 + 360 = 530.
• Question 2

Select all the trigonometric ratios which are equal to one another.

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

Select all the trigonometric ratios which are equal to one another.

cos 190°
-cos 10°
cos 550°
EDDIE SAYS
The 190° line makes an angle of 10° with the horizontal.
190° is in the 3rd quadrant where cos is negative.
190 + 360 = 550.
• Question 4

Select all the trigonometric ratios which are equal to one another.

tan 10°
tan 190°
tan 550°
EDDIE SAYS
The 190° line makes an angle of 10° with the horizontal.
190° is in the 3rd quadrant where tan is positive.
190 + 360 = 550.
• Question 5

Select all the trigonometric ratios which are equal to one another.

-tan 70°
tan 110°
tan 470°
EDDIE SAYS
The 110° line makes an angle of 70° with the horizontal.
110° is in the 2nd quadrant where tan is negative.
110 + 360 = 470.
• Question 6

Select all the trigonometric ratios which are equal to one another.

sin 135°
sin 45°
sin 495°
EDDIE SAYS
The 135° line makes an angle of 45° with the horizontal.
135° is in the 2nd quadrant where sin is positive.
135 + 360 = 495.
• Question 7

Select all the trigonometric ratios which are equal to one another.

cos 35°
cos 325°
cos 685°
EDDIE SAYS
The 325° line makes an angle of 35° with the horizontal.
325° is in the 4th quadrant where cos is positive.
325 + 360 = 685.
• Question 8

Select all the trigonometric ratios which are equal to one another.

cos 245°
-cos 65°
cos -115°
cos 605°
EDDIE SAYS
The 245° line makes an angle of 65° with the horizontal.
245° is in the 3rd quadrant where cos is negative.
245 + 360 = 605.
245 - 360 = -115
• Question 9

Select all the trigonometric ratios which are equal to one another.

-tan 55°
tan 125°
tan 845°
EDDIE SAYS
The 125° line makes an angle of 55° with the horizontal.
125° is in the 2nd quadrant where tan is negative.
125 + 720 = 845.
• Question 10

Select all the trigonometric ratios which are equal to one another.

sin 222°
sin -138°
-sin 42°
EDDIE SAYS
The 222° line makes an angle of 42° with the horizontal.
222° is in the 3rd quadrant where sin is negative.
222 - 360 = -138.
---- OR ----

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