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sin312 the terminal angle of 312 is equal to 48 degrees! That's all i know!

Q: How to express sin of an angle in terms of the terminal angle?

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Example: Express sin 120⁰ as a function of an acute angle (an angle between 0⁰ and 90⁰).Solution:Each angle θ whose terminal side lies in quadrant II, III, or IV has associated with it an angle called the reference angle, alpha (alpha is formed by the x-axis and the terminal side).Since 120⁰ lies on the second quadrant, then alpha = 180⁰ - 120⁰ = 60⁰.Since sine is positive in the second quadrant, sin 120⁰ = sin 60⁰.Example: Express tan 320⁰ as a function of an acute angle.Solution:Since 320⁰ lies on the fourth quadrant, then alpha = 360⁰ - 320⁰ = 40⁰.Since tangent is negative in the fourth quadrant, tan 320⁰ = -tan 40⁰.

sin(x) = [1 + cot^2(x)]^-0.5

There is no such angle, since the sine of an angle cannot be greater than 1.

To simplify such expressions, it helps to express all trigonometric functions in terms of sines and cosines. That is, convert tan, cot, sec or csc to their equivalent in terms of sin and cos.

nwater * sin 30=nair *sin(angle of refraction) 1.33*0.5=1*sin(angle of refraction) sin(angle of refractiob)=0.665 angle of refraction inair=41.6 degrees nwater * sin 30=nair *sin(angle of refraction) 1.33*0.5=1*sin(angle of refraction) sin(angle of refractiob)=0.665 angle of refraction inair=41.6 degrees

write in terms of sin, cos or tan then use the double angle formulae. I.e. cosec(x)=1/sin(x) =1/[2sin(x)cos(x)]

type the value of sine in the calculator and press 2ND SIN for sin-1, or press 2ND SIN for sin-1 and type the value of sine, because -sin(.xxxx) = angle known as inverse sine

This question is ambiguous. If you have an original side, and you know the terminal (final) side, and you know the terminal angle (between the two sides), then there's really not that much more. For rectangular coordinates (x and y) of offsets, use sines and cosines. Vertical offset is (terminal sidelength)*sin(DEGREE MEASURE) Horizontal offeset is (terminal sidelength)*cos(DEGREE MEASURE)

-- sin(x) is a number. It's the sine of the angle 'x'. -- sin-1(x) is an angle. It's the angle whose sine is the number 'x'.

(sin x + cos x) / cosx = sin x / cos x + cosx / cos x = tan x + 1

sin2(1) = 1 - cos2(1) = 1 - [cos(1)]2

Sin(285) is a number, not an angle. The reference angle for 285 degrees is 285-360 = -75 degrees.