SOLUTION: Hi, Looking for help with these problems. 1: The equation of the line passing through the point (1,-2) and perpendicular to the line Y=(-2/3X)+(4/3)is? 2: Simplify the expressio

Question 148144: Hi,
Looking for help with these problems.
1: The equation of the line passing through the point (1,-2) and perpendicular to the line Y=(-2/3X)+(4/3)is?
2: Simplify the expression below (leave answer with positive exponents)
(7X^3Y/14XY^-2)^2 both numerator & denominator squared.
3: The trigonometric expression SinӨ+CotӨCosӨ
4: If SinӨ=(3/5) and Ө is in quadrant2 find Sin2Ө (Hint Sin2Ө=SinӨCosӨ)
Last one for trig! yes!
5: The point (-2,3) lies on the terminal side of an angle Ө in standard position. Find the exact value of Ө.
Thank YOU!!!!!!!!!!!!!!!!!!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1: The equation of the line passing through the point (1,-2) and perpendicular to the line Y=(-2/3X)+(4/3)is?
-----------------------------------
slope = 3/2
Form: y = mx + b
You know m=3/2 and y = -2 when x = 1 ; solve for "b":
-2 = (3/2)*1 + b
b = -7/2
EQUATION: y = (3/2)x - (7/2)
===================================
2: Simplify the expression below (leave answer with positive exponents)
(7X^3Y/14XY^-2)^2 both numerator & denominator squared.
Cancel the common factors: 7, X
= (X^2Y^5/2)^2
= (X^4 y^10 / 4)
============================

3: The trigonometric expression
SinӨ+CotӨCosӨ = sin(theta) + [cos(theta)/sin(theta)]*cos(theta)
= sin(theta) + cos^2(theta)/sin(theta)
= [sin^2(theta) + cos^2(theta)]/sin(theta)
= 1/sin(theta)
= csc(theta)
============================
4: If SinӨ=(3/5) and Ө is in quadrant2 find Sin2Ө (Hint Sin2Ө=SinӨCosӨ)
In 2nd Quadrant, if sin=43/5, cos=-4/5
Then sin(2theta)= (3/5)(-4/5) = -12/25
============================
5: The point (-2,3) lies on the terminal side of an angle Ө in standard position. Find the exact value of Ө.
theta = tan^-1(-3/2) = -56.31 degrees = 180 = 123.31 degrees
=======================================
Cheers,
Stan H.

RELATED QUESTIONS
Hi, can anyone help figure out these two coordinate geometry problems?: 1) How do I... (answered by Alan3354)

Hi everyone, Im looking for some help and guidance with the following graphing and... (answered by solver91311)

Hi everyone, Im looking for some help and guidance with the following graphing and... (answered by rfer)

Hi, I'm having some trouble with perpendicular lines, Can you help me? Find an... (answered by solver91311)

Find the equation of the line passing through the point (2, 1) and perpendicular to the (answered by solver91311,Alan3354)

Find the equation of the line passing through the point (2, 1) and perpendicular to the... (answered by josgarithmetic)

Find the equation of the line passing through the point (2, 1) and perpendicular to the... (answered by stanbon)

Choose the equation of the line passing through the point (-1, -2) and perpendicular to y (answered by lwsshak3)