Trigonometry Answers

In the diagram below, ab and ac are phasors representing the alternating currents in two branches of a circuit. The line ac represents the resultant current. Find the resultant current.
Description of the diagram:
right angled triangle labelled a, b, c
line AB has 15A and line BC has 10A
the angle is 40 degrees

If the wind speed is 60 mph and the velocity due to the thrust is 500 mph show that the resultant velocity R is
a. at an angle of 6.84 degrees to the thrust of the engines and
b. is about 504 mph
Show all working.

cosec2A-cot2A

sinAsin(60-A)sin(60+A)=1/4sin3A

what is the actual value of arc sin (-15/17) + arc sin (-30/36) . use arc sin x + arc sin y formula

what is the actual value of , arc tan [(-1)/(1)] , arc tan [(1)/(-1)] . do they have different value? then why ? both looks like arc tan [-1] which is -pi/4 . so now what is the actual value of arc sin [(-15)/(17)] , arc tan [(15)/(-17)] . do they have different value like arc tan or do they have same value ? then why ???

If arc sin x +arc sin y +arc sin z = pi . prove that [x *sqrt(1-x^2)] +[y *sqrt(1-y^2)]+[z *sqrt(1-z^2)] = 2xyz. show the process please

What is the actual value of arc sin(12/13) +arc sin(4/5)+arc sin(1). show the process using arc sinx +arc sin y formula?


using formula for the first two it comes pi - arc sin (56/65) then + arc sin 1 which is pi/2 . so the final result is 3pi/2 - arc sin (56/65) . and if i dont write pi/2 instead of arc sin 1 , then the result is pi - arc sin (56/65) +arc sin 1 = pi + arc sin (33/65) using formula for arc sin 1 - arc sin (56/65). i m lil bit confused which one is correct ? is there any use of principal value

the calculator shows its approximately 210 degree , means its a third quadrent angle .

normally we know arc sinx +arc sin y = arc sin [x*sqrt(1-y^2) +y*sqrt(1-x^2)]. but if we use this , the answer comes arc sin (56/65) + pi/2 , which does not match with the calculator result . so is there any regulation for arc sinx +arc sin y formula and is it applicable for (arc sinx +arc sin y) < pi/2 ?????

Without using tables or calculator,find the value of :
cos 900+1.

A 1
B 8
C 3
D2

Without using tables , find the value of sin600cos600

A 3√
B 3
C 1
D4√