Mar 7, 2018 · sin (-90) = -1 sin -90 = sin (360 - 90) = sin 270 Angle 270^@ is third quadrant, where only tan and cot are positive.

Dec 17, 2015 · Use the sine angle subtraction formula: #sin(alpha-beta)=sin(alpha)cos(beta)-cos(alpha)sin(beta)# Therefore, #sin(x-90˚)=sin(x)cos(90˚)-cos(x)sin(90˚)#

Jun 27, 2019 · => sin(90 + x) = cos(x) [ replace y with x] If you replace x with -x in the above equation you get sin(90 - x) = cos(-x) => sin(90 - x) = cos(x) [as cos(-x) = cos(x)] More …

Jun 30, 2016 · We know the angles in a right triangle, and a triangle in general, must add to 180^o, so if we have an angle of 90 and an angle of a, our other angle must be 90-a: (a)+(90 …

Aug 14, 2015 · A shift of -90 degrees of sin x gives you cos x Method 2: sin (A +- B) = sin A cos B +- cos A sin B .

Dec 11, 2020 · $\begingroup$ That's why others have given the answers that really show you why is $\sin(90^{\circ})=1$. What I have shown to you is according to your wish from a triangle's …

Apr 8, 2019 · If you have a definition of each function that is valid on angles outside the range $0$ to $90$ degrees, you can derive formulas for things such as $\sin(\theta + 90^\circ).$ But you …

Dec 29, 2020 · As $\theta \to 90^\circ$, $\frac{O}{H} \to 1$.Because O and H become closer and closer to the same value. You can see that on your graph (just keep track of the colors, red …

May 13, 2015 · Consider that -90° corresponds to 270° (the minus sign is to turn clockwise instead of counter-clockwise): so: sin(-90°)=sin(270°)=-1

$\begingroup$ Because if you let the hypotenuse be C the side adjacent to angle a be A and the side adjacent to angle 90-a be B you have sin(90-a)= A/C and cos(a)=A/C by trigonometric …