2018年3月7日 · sin −90 = sin(360 − 90) = sin270 Angle 270∘ is third quadrant, where only tan and cot are positive. Hence sin270 = sin(180 +90) = − sin90 = −1

2019年6月27日 · 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.

2015年12月17日 · Use the sine angle subtraction formula: sin(α −β) = sin(α)cos(β) −cos(α)sin(β) Therefore, sin(x − 90˚) = sin(x)cos(90˚) − cos(x)sin(90˚) = sin(x)(0 ...

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 · As θ → 90∘ θ → 90 ∘, O H → 1 O H → 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). Another way to look at it is by generalizing the trigonometric functions beyond side lengths of triangles.

2016年6月30日 · I prefer a geometric proof. See below. If you're looking for a rigorous proof, I'm sorry - I'm not good at those. I'm sure another Socratic contributor like George C. could do something a little more solid than I can; I'm just going to give the lowdown on why this identity works. Take a look at the diagram below: It's a generic right triangle, with a 90^o angle as indicated by the little box ...

2020年12月11日 · If you a want to know how is sin(90∘) = 1 sin (90 ∘) = 1 from a triangle's point of view, well you can take any right angled triangle and fix the base length. Now increase the perpendicular side. You will see that as you increase the …

2019年4月8日 · Then sin(θ) sin (θ) is the y y coordinate of the point you reached at the end of that path, and cos(θ) cos (θ) is the x x coordinate of that same point. Now let's try to find the sine of (π2 + θ) (π 2 + θ) radians, that is, the sine of 90 90 degrees plus θ θ radians.

2015年4月17日 · Note that the image below is only for x in Q1 (the first quadrant). If you wish you should be able to draw it with x in any quadrant. Definition of sin(x) (side opposite angle x)/(hypotenuse) Definition of cos(90∘ −x) (side adjacent to angle (90∘ − x))/(hypotenuse) but (side opposite angle x) = (side adjacent to angle (90∘ − x ...

2015年8月14日 · sin(90 +x) = cosx Method 1: Using plots of sinx and cosx. A shift of -90 degrees of sinx gives you cosx Method 2: sin(A± B) = sinAcosB ± cosAsinB