2018年3月7日 · sin (-90) = -1 sin -90 = sin (360 - 90) = sin 270 Angle 270^@ is third quadrant, where only tan and cot are positive.

2019年6月27日 · => 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 ...

2015年12月17日 · 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˚)#

2015年8月14日 · 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 .

2016年6月30日 · 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.

2020年12月11日 · $\begingroup$ 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.

2019年4月8日 · 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? $\endgroup$ –

2015年5月13日 · Consider that -90° corresponds to 270° (the minus sign is to turn clockwise instead of counter-clockwise): so: sin(-90°)=sin(270°)=-1

2020年12月29日 · Improving my way of showing $\sin^212^\circ+\sin^221^\circ+\sin^239^\circ+\sin^248^\circ=1+\sin^29^\circ+\sin^218^\circ$ Hot Network Questions Why does Trump expect closing the Dept. of Education and returning education authority to the states will improve the quality of the school system?

$\begingroup$ 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. $\endgroup$ –