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1. In what interval(s) between 0 and 2pi are tan(theta) and sin(theta) both negative? Both positive?
2. Find all angle measures between 0 degrees and 360 degrees for which the sin of theta = -0.55
3. Find two values of theta on the interval 0 is less than or equal to theta which is less than or equal to 360 degrees that satisfy the equation tan = -.08693.
1. In what interval(s) between 0 and 2pi are tan(theta) and sin(theta) both negative? Both positive?
2. Find all angle measures between 0 degrees and 360 degrees for which the sin of theta = -0.55
3. Find two values of theta on the interval 0 is less than or equal to theta which is less than or equal to 360 degrees that satisfy the equation tan = -.08693.
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1. Since Tan() = Sin()/Cos(), Tangent is negative where Sine and Cosine are of opposite signs. That’s Q2 and Q4, or π/2 < < 3 π/2. Q1 and Q3 are the quadrants where Sine is positive. It is all the rest.
2. Solve, Sin() = -0.55, so = ArcSin(-0.55) = -33.37° = 326.63° or 213.364.
3. Do you mean Tan() = -0.08693? = ArcTan(-0.08693) = -4.968° = 355.032° or = 175.032°
The first value of is the principal root of the arc-function. The others are found by knowing the quadrants that function is the appropriate sign.
PS: All of this is in your textbook, but you have to read it!!!!
is suppose to be theta.
2. Solve, Sin() = -0.55, so = ArcSin(-0.55) = -33.37° = 326.63° or 213.364.
3. Do you mean Tan() = -0.08693? = ArcTan(-0.08693) = -4.968° = 355.032° or = 175.032°
The first value of is the principal root of the arc-function. The others are found by knowing the quadrants that function is the appropriate sign.
PS: All of this is in your textbook, but you have to read it!!!!
is suppose to be theta.