1 Over Sin Math

Sine cosine and tangent.

1 over sin math. The exact value of is. Sin 1 y q y 1 csc y q cos 1 x q x 1 sec x q tan y x q cot x y q facts and properties domain the domain is all the values of q that can be plugged into the function. And cosine and tangent follow a similar idea. For a given angle θ each ratio stays the same no matter how big or small the triangle is.

Sin θ bc. Ag 1 cos θ sin θ cos θ ag 1 sin θ. The deriviative d dxsin x at x 0 is also 1 this means you have the division of two functions sin x and x at a point where their slope is the same so the limit reduces to 1 over 1 which is 1. Sin theta 1 take the inversesineof both sides of the equationto extract from inside the sine.

Students teachers parents and everyone can find solutions to their math problems instantly. Free math lessons and math homework help from basic math to algebra geometry and beyond. Sine cosine and tangent often shortened to sin cos and tan are each a ratio of sides of a right angled triangle. Secant cosecant and cotangent almost always written as sec cosec and cot are trigonometric functions like sin cos and tan.

Cosec x 1 sin x cot x 1 cos x tan x sin x. The inverse sine function sin 1 takes the ratio oppositehypotenuse and gives angle θ. Note that the three identities above all involve squaring and the number 1 you can see the pythagorean thereom relationship clearly if you consider the unit circle where the angle is t the opposite side is sin t y the adjacent side is cos t x and the hypotenuse is 1. Ag 1 sec θ tan θ.

This one diagram beautifully depicts the geometrical meaning of all six trig functions when the angle θ is drawn at the center of a unit circle. Ag csc θ. Sec θ ae. We have additional identities related to the functional status of the trig ratios.

Divide the length of one side by another side. The sinefunctionis positive in the first and secondquadrants. Cot θ fg. Sec x 1 cos x.

Tan θ ed. Sinq q can be any angle cosq q can be any angle tanq 1 0 1 2 2 qpnn.