stuck with a level maths concept

9

Hi, I am struggling to understand the concept of this (see attachment). I am unsure when there is a positive and when there is a negative I don't really understand what this is meaning. Can someone please explain it to me so that I understand it better. Thanks! Screenshot 2025-05-06 202206.png

Reply 1

mqb2766

21

Original post

by kyefrankie

Hi, I am struggling to understand the concept of this (see attachment). I am unsure when there is a positive and when there is a negative I don't really understand what this is meaning. Can someone please explain it to me so that I understand it better. Thanks! Screenshot 2025-05-06 202206.png

There are a few things on the cast diagram so

•

Trig functions repeat (periodic) every 360 and you can think of the angles lying between 0 and 360 or -180 and 180. Postive angles are measured from the positive x-axis anticlockwise and negative angles are mesured from the positive x-axis clockwise.

•

Think of the x-axis as cos and the y-axis as sin. Then cos() is positive for angles to the right of the y-axis so -90 to 90 and sin() is positive for angles above the x-axis so 0 to 180. So in Q1 both trig functions are positive, Q2 sin is positive, cos is negative, Q3 both are negative and Q4 cos is positive and sin negative.

•

There are symmetries in the cos() and sin() functions. cos() has the same value for the two angles which are reflected in the x-axis (so about 0 and 180 degrees). So +/-30 have the same cos() value and +/-150 have the same cos() value. sin() has the same value for the two angles which are reflected in the y axis (so about 90 and 270). So 60 and 120 have the same sin() value and 240 and 300 have the same sin() value.

•

Tan defined by sin/cos, but it has the same value (gradient) for the two angles which are 180 apart and correspond to a line passing through the origin.

Reply 2

kyefrankie

OP

9

Original post

by mqb2766

There are a few things on the cast diagram so

•

Trig functions repeat (periodic) every 360 and you can think of the angles lying between 0 and 360 or -180 and 180. Postive angles are measured from the positive x-axis anticlockwise and negative angles are mesured from the positive x-axis clockwise.

•

Think of the x-axis as cos and the y-axis as sin. Then cos() is positive for angles to the right of the y-axis so -90 to 90 and sin() is positive for angles above the x-axis so 0 to 180. So in Q1 both trig functions are positive, Q2 sin is positive, cos is negative, Q3 both are negative and Q4 cos is positive and sin negative.

•

There are symmetries in the cos() and sin() functions. cos() has the same value for the two angles which are reflected in the x-axis (so about 0 and 180 degrees). So +/-30 have the same cos() value and +/-150 have the same cos() value. sin() has the same value for the two angles which are reflected in the y axis (so about 90 and 270). So 60 and 120 have the same sin() value and 240 and 300 have the same sin() value.

•

Tan defined by sin/cos, but it has the same value (gradient) for the two angles which are 180 apart and correspond to a line passing through the origin.

okay thank you I'm beginning to understand. One thing i forgot to mention is that im doing the year 2 book and am doing it in radians. I can kind of relate it to the points you said about degrees eg 90 degrees is pi/2 and 180 degrees is pi 270 degrees is 3pi/2 and 360 degrees is 2pi. could you talk me through the first couple questions here so i can fully understand what im doing. Thanks! Screenshot 2025-05-06 204655.png

Reply 3

mqb2766

21

Original post

by kyefrankie

okay thank you I'm beginning to understand. One thing i forgot to mention is that im doing the year 2 book and am doing it in radians. I can kind of relate it to the points you said about degrees eg 90 degrees is pi/2 and 180 degrees is pi 270 degrees is 3pi/2 and 360 degrees is 2pi. could you talk me through the first couple questions here so i can fully understand what im doing. Thanks! Screenshot 2025-05-06 204655.png

Sure, whether its degrees or radians the arguments are the same. For sin() for instance which is symmetric for reflections in the y-axis so pi/2 or 3pi/2 you should be able to sketch the normal sin() curve and note that the curve is symmetric about those two values (when sin=+/-1) so if youre unsure with cast, sketching the usual trig curves is recommended.

But for a) say, Id draw the angle 3pi/4 or 135 degrees and as its sin() you want its reflection in the y-axis so ...

b) is similar so draw the angle -pi/3 or -60 degrees and as its sin() and below the x-axis note the sign so ...

(edited 9 months ago)

stuck with a level maths concept

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