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 explanation - sin and cos are complementary to each other, that's where the name came from - sine and cosine . Complementary angles in a triangle are x and 90-x. So, sin ...

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-a)+(90)=180 180=180 We can see that the angles in our triangle do indeed add to 180, so we're on the right track. Now, let's add some variables for side length onto our triangle.

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 perspective. This shows that $\sin(89.99\cdots)$ tends to $1$. Of course, you can't apply pythagoras theorem here as a triangle with two $90$ degree angles cannot form.

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 need a definition first. Is the unit circle definition acceptable? $\endgroup$ –

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 and green are overlapping).

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 ratios. $\endgroup$ –