2016年3月7日 · #cos(x)sin(x)# If we multiply it by two we have #2cos(x)sin(x)# Which we can say it's a sum. #cos(x)sin(x)+sin(x)cos(x)# Which is the double angle formula of the sine. #cos(x)sin(x)+sin(x)cos(x)=sin(2x)# But since we multiplied by 2 early on to get to that, we need to divide by two to make the equality, so. #cos(x)sin(x) = sin(2x)/2#

2015年4月15日 · Please see two possibilities below and another in a separate answer. Explanation: Using Pythagorean Identity. #sin^2x+cos^2x=1#, so #cos^2x = 1-sin^2x#

2017年11月20日 · See below. As can be seen the graphics for cos(cos(cos(x))) (blue) and sin(sin(sin(x))) (red) intersect in two points for -pi le x le pi NOTE: As we can easily verify 0.540302 approx cos(1) le cos(cos(cos(x))) le cos(cos(1)) approx 0.857553 and -0.745624 approx -sin(sin(1)) le sin(sin(sin(x))) le sin(sin(1)) approx 0.745624 and for x = pi/2 we have …

2018年4月6日 · #sin^2x-cos^2x# The key realization is that the original expression in question was in a difference of squares pattern. If you have a #(a-b)(a+b)# pattern, you can always use the difference of squares identity to quickly simplify it.

"The fundamental trigonometric identities" are the basic identities: •The reciprocal identities •The pythagorean identities

2016年3月18日 · pi/4 sin x = cos (pi/2 - x) --> complementary arcs Therefor, cos (pi/2 - x) = cos x (pi/2 - x) = +- x a. pi/2 - x = x --> 2x = pi/2 --> x = pi/4 b. pi/2 - x = - x ...

The functions sine, cosine and tangent of an angle are sometimes referred to as the primary or basic trigonometric functions.

2016年5月27日 · cot(x) cos(x)/sin(x) = cot(x) How do you apply the fundamental identities to values of #theta# and show that they are true?

2015年8月5日 · Reminder: cos (-x) = cos x and sin (-x) = -sin x The trig expression results in: cos^2 x + sin^2 x = 1

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) Therefore sin(x) = cos(90^@ -x) …