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enter image description here

This is the image my textbook uses for finding whether the ratios are +ve or -ve.

Here , i feel they mean to say that tan (+x) = tan x since b and a are +ve . We can tell it by looking at the x and y axis But I want to know if they talk about sin(+x) , how do we know if OP is +ve or not.

Can we also say that x = 1 since it is a radian measure of 1 unit.

Rider
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  • An easier method is that the coordinates of a point on the unit circle (the circle of radius $1$ centered at the origin) are $(\cos \theta, \sin\theta)$ where $\theta$ is the angle measured counterclockwise from the positive $x$-axis. – saulspatz Apr 13 '21 at 08:15

1 Answers1

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How do we know if OP is +ve or not?
In the unit circle, OP is always defined as positive.

Can we also say that x = 1 since it is a radian measure of 1 unit?

Remember the definition of $s = r \times \theta$ . When $ s =x, r = 1,\theta = x, x=1 \times x$, can we draw conclusion x=1?

How do we find the signs of trig ratios?

The following trig plots are very helpful to understand the signs of trig ratios. Just play through the link. Once you understand it, you do not need to remember it.

$\color{blue}{Blue}: \sin \theta: >0 (Q1,2), <0 (Q3,4)$

$\color{red}{Red}: \cos \theta: >0 (Q1,4), <0 (Q2,3)$

$\color {pink}{Pink}: \tan \theta: >0 (Q1,3), <0 (Q2,4)$

enter image description here

Star Bright
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  • Amazing it is. Thanks a lot. https://math.stackexchange.com/q/4100701/883022 Pls do take a look. – Rider Apr 13 '21 at 17:12