If the sin of angle A is 13 then the cosine of that angle is

If the sin of angle A is 1/3, then the cosine of that angle is ______ Given tan of angle A is -3/4, and ends in quadrant 2, then the cosine of angle A is _____ Arc cos( squareroot 2/2), also represented as cos^-1 ( squareroot 2/2) is ______ [Assume the angle is in Quadrant 1]

Solution

6. SInA=1/3

Here oppsoite=1 and hypotenuse= 3

Therefore adjacent=sqrt(3²-1)=2sqrt2

cos A= adjacent/hypotenuse= 2sqrt2/3

7. tan A= -3/4

here opposite=3   and   adjacent=4

hypotenuse= sqrt(4²+3²)= 5

cosine is negative in second quadrant

Therefore cos A= adjacent/hypotenuse=-4/5