Let m∠CLN = x. Then m∠ALM = 3x, and m∠A = 90°-x, m∠C = 90°-3x.
The sum of angles of ∆ABC is 180°, so we have
... 180° = 40° + m∠A + m∠C
Using the above expressions for m∠A and m∠C, we can write ...
... 180° = 40° + (90° -x) + (90° -3x)
... 4x = 40° . . . . . . . . . add 4x-180°
... x = 10°
From which we conclude ...
... m∠C = 90°-3x = 90° - 3·10° = 60°
The ratio of CN to CL is
... CN/CL = cos(∠C) = cos(60°)
... CN/CL = 1/2
so ...
... CN = (1/2)CL
Step-by-step explanation:
Let the complex numbers be .
Given, sum is , difference is
and product is
.
⇒
⇒
Hence, all three equations are consistent yielding the complex numbers .
Answer:
<em>A) The reference angle should be </em><u><em>,</em></u><em> and the sign of the value should be </em><u><em>negative.</em></u>
Step-by-step explanation:
cos()
Remove full rotations of 2π until the angle is between 0 and 2.
cos()
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.
-cos()
The exact value of cos() is
.
−