Solve the eqn 25 cos x = 16 sin x tan x for 0 < or = x < or = 360. Could anyone help me on this?

1 Answer
Apr 26, 2018

The exact answer is

# x = arctan(pm 5/4) #

with approximations #x = 51.3^circ, 231.3^circ, 308.7 ^circ # or # 128.7^circ.#

Explanation:

# 25 cos x = 16 sin x tan x#

#25 cos x = 16 sin x \frac{sin x}{cos x}#

# 25/16 = {sin^2 x}/{cos ^2 x} = tan^2 x#

#tan x = \pm 5/4 #

At this point we're supposed to do approximations. I never like that part.

#x = arctan(5/4) approx 51.3°#

# x approx 180^circ + 51.3^ circ = 231.7^circ #

# x approx -51.3^circ + 360 ^circ = 308.7 ^circ#

# or x approx 180^circ + -51.3 = 128.7^circ#

Check:

# 25(cos(51.3)) - 16(sin(51.3) tan (51.3)) = -.04 quad sqrt#

# 25(cos(231.3)) - 16(sin(231.3) tan (231.3)) = -.04 quad sqrt#

I'll let you check the others.

enter image source here