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3 years ago

If cos θ =-2/5 and tan θ > 0, what is the value of sin θ?

1 answer:

8 0

If the value of cos(θ) is negative, this angle (θ) can only be in one of two quadrants; the sine quadrant or the tan quadrant. In the sine quadrant, tan(θ) must be negative, but since tan(θ) > 0, we can safely say that the angle (θ) is based in the tan quadrant.

We know that cos(θ) = - Adjacent / Hypotenuse, and in this case Adjacent = 2 and Hypotenuse = 5. Using Pythagoras' theorem, we can find the opposite side of the right angled triangle situated in the tan quadrant...

Adjacent² + Opposite² = Hypotenuse²

Therefore:

2² + Opposite² = 5²

Opposite² = 5² - 2²

Opposite² = 21

Opposite = √(21)

------------

Now, sin(θ) must be negative, as the right angled triangle is in the tan quadrant. We also know that sin(θ) = Opposite / Hypotenuse, therefore:

sin(θ) = - [√(21)]/[5]

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4 years ago

Cathy Woolfrey is buying a new home. Her realtor tells her that the home she is buying has increased in price by 10% since it wa

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Answer:

The Price of Home last time it was sold is $2,000,00

Step-by-step explanation:

Given as ,

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Now , Let the last price be = $ x

Again AS per question ,

x + 10% of x = $220,000

x + $\frac{10}{100}$ × x = $220,000

( $\frac{110}{100}$ ) × x = $220,000

Or, x = ( $\frac{220,0000}{11}$ )

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Hence the Price of Home last time it was sold is $2,000,00 Answer

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3 years ago

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4 years ago

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E. Find the length of sides of the triangle whose vertices are A (7,4), B (-8, 6) Ć(1, -3).

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Answer:

Length of sides of triangle are: AB = 15.13, BC = 12.72, AC = 9.21

Step-by-step explanation:

We need to find the length of sides of the triangle whose vertices are A (7,4), B (-8, 6) C(1, -3).

We have three sides of triangle AB, BC and AC

The length of side can be calculated using distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Now finding lengths of sides AB, BC and AC

i) Length of side AB

We have A (7,4), B (-8, 6)

and $x_1=7, y_1=4, x_2=-8, y_2=6$

Putting values in formula and finding length

$Length \ of \ side \ AB \ =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Length \ of \ side \ AB \ =\sqrt{(-8-7)^2+(6-4)^2}\\Length \ of \ side \ AB \ =\sqrt{(-15)^2+(2)^2}\\Length \ of \ side \ AB \ =\sqrt{225+4}\\Length \ of \ side \ AB \ =\sqrt{229}\\Length \ of \ side \ AB \ =15.13$

So, Length of side AB is 15.13

ii) Length of side BC

We have B (-8, 6) and C(1, -3)

and $x_1=-8, y_1=6, x_2=1, y_2=-3$

Putting values in formula and finding length

$Length \ of \ side \ BC \ =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Length \ of \ side \ BC \ =\sqrt{(1-(-8))^2+(-3-6)^2}\\Length \ of \ side \ BC \ =\sqrt{(1+8)^2+(-9)^2}\\Length \ of \ side \ BC \ =\sqrt{(9)^2+(-9)^2}\\Length \ of \ side \ BC \ =\sqrt{81+81}\\Length \ of \ side \ BC \ =\sqrt{162}\\Length \ of \ side \ BC \ =12.72$

So, Length of side BC is 12.72

iii) Length of side AC

We have A (7,4)and C(1, -3)

and $x_1=7, y_1=4, x_2=1, y_2=-3$

Putting values in formula and finding length

$Length \ of \ side \ AC \ =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Length \ of \ side \ AC \ =\sqrt{(1-7)^2+(-3-4)^2}\\Length \ of \ side \ AC \ =\sqrt{(-6)^2+(-7)^2}\\Length \ of \ side \ AC \ =\sqrt{36+49}\\Length \ of \ side \ AC \ =\sqrt{85}\\Length \ of \ side \ AC \ =9.21$

So, Length of side AC is 9.21

So, length of sides of triangle are: AB = 15.13, BC = 12.72, AC = 9.21

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3 years ago