if cot Ø =5, and cos Ø < 0, what is sin Ø?
ecos (20) cos e Establish the identity cos + cos (30) sin 0+ sin (30) cot (20) Choose the correct sequence of steps to establish the identity cos 0 + cos (30) 2 cos (20) cos (20) OA sin 0+ sin (30) cot (20) 2 cos (20) sin (20) B. cos 0 + cos (30) sin 0 + sin (30) = 2 sin (20) cos e = cot (20) Ос. = cos 0 + cos (30) 2 sin cos (20)...
cos(O) cot(0) = csc(O) – sin(e) Rewrite cotangent in terms of sine and cosine: cos(O) cot(O) = cos(0) · Rewrite as a single fraction: Use a Pythagorean identity: sin(0) Finally, separate the fraction into two: sin(e) sin(e) = csc(0) – sin(0)
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ < T* 2 marks (a) Describe this region. an appropriate integration, determine the volume of this shape [4 marks (b) Using 3 (Continued) 3 marks (c) Parametrise the surface of this shape. 3 marks (d) Find a normal to the surface [4 marks (e) What is the surface area of...
Ein the identity. sin(a+B) = tan a cot +1 cos a sin B Choose the sequence of steps below that verifies the identity. O A. sin (a +B) cos a sin cos acos B+ sin a sin cos a sin B cos acos B cos a sin B + sin a sin cos a sin = tan a cot B+1 sin a cos B+ cos a sin B cos a sin sin a cos p cos a sin + cos...
Establish the identity sin 20(1+cot ?0) = 1 Which of the following shows the key steps in establishing the identity? 1 sin 20 ОА. sin ?е(1 + cot?e) = sin 20 tan 20= sin 20- cot20 sin 20 O B. sin 20(1 + cot 20) = sin 20+ sin 20 cot 20= sin 20+ cos20= 1 Ос. sin 20(1+ cot?e) = cos 20+ cos 20 sin de + cos20 = 1 sin e cos 20 D. 1 sin 20 sin...
Find sin(a) and cos(B), tan(a) and cot(B), and sec(a) and cSC(B). a 14 B (a) sin(a) and cos() (b) tan(a) and cot(6) (c) sec(a) and csc()
If sin(0) = -5, and 0 is in quadrant IV, then find: (a) cos(0) = C Preview (b) tan(0) = 0 Preview (C) sec(0) = O Preview (d) csc(0) = 0 Preview (e) cot(0) = C Preview)
prove the identities
g. CSC A-sin A = cos A cot A Solution:
3 12 Smaller Triangle Larger Triangle sin = sin = cos = cos = tan 0= tan (= CSC = CSC = sec = sec = cot 8 = cot = Explain why the function values are the same. The triangles are similar so corresponding sides are proportional. The triangles are congruent so the trigonometric function values must be the same.
cot(theta)=-3/4 and cos(theta)
7. cot(0) - 3 4 and cos(0) <0, find the exact value of sec(0)