Find the dot product for the pair of vectors 7i 6j 10i 7j

Find the dot product for the pair of vectors. -7i + 6j, 10i - 7j Write the complex number 3 + 4i in trigonometric form r(cos theta + I sin theta), with theta in the interval [0 degree, 360 degree) Find the period of y = -3 cos 1/4 x Find the exact value of y = sin^-1 (-0.5)

Solution

v1 = -7i +6j ; v2 = 10i - 7j

Dot product = v1.v2 = (-7i +6j)(10i -7j) = -70 -42 = -112

y = -3cos(x/4)

period = 2pi/ (1/4) = 8pi

y = sin^-1(-0.5)

Range of sin^-1(x) : [ -pi/2 , pi/2 ]

y = sin^-1(-0.5)

siny = -0.5

y = -pi/6