The exact values of the remaining <u>five</u> trigonometric functions of theta are
- sinθ = √3/2
- cosecθ = 2/√3
- cosθ = -1/2
- secθ = -2
- cotθ = -1/√3
Since tanθ = -√3.
The remaining <u>five</u> trigonometric functions of theta are sinθ, cosecθ, cosθ, secθ and cotθ.
The next trigonometric function of θ is cotθ.
cotθ = 1/tanθ
= 1/-√3
= -1/√3.
Also, tan²θ + 1 = sec²θ
Substituting tanθ = -√3 into the equation, we have
(-√3)² + 1 = sec²θ
3 + 1 = sec²θ
sec²θ = 4
secθ = ±√4
secθ = ±2
Since θ is in the quadrant II,
secθ = -2
Also, cosθ = 1/secθ
= 1/-2
= -1/2
Also, cot²θ + 1 = cosec²θ
Substituting cotθ = -1/√3 into the equation, we have
(-1/√3)² + 1 = cosec²θ
1/3 + 1 = cosec²θ
cosec²θ = 4/3
cosecθ = ±√(4/3)
cosecθ = ±2/√3
Since θ is in the quadrant II,
cosecθ = +2/√3
Also, sinθ = 1/cosecθ
= 1/2/√3
= √3/2
So, the exact values of the remaining <u>five</u> trigonometric functions of theta are
- sinθ = √3/2
- cosecθ = 2/√3
- cosθ = -1/2
- secθ = -2
- cotθ = -1/√3.
Learn more about trigonometric functions here:
brainly.com/question/4515552
What percentage of its capacity is 9 people?
<em> 12%</em>
What percentage of its capacity is 51 people?
<em> 68 %</em>
What percentage of its capacity is 84 people?
<em>112%</em>
<h2>
It is an obtuse angle.</h2>
Step-by-step explanation:
Obtuse: An obtuse angle is an angle more than 
but less than 
.
Example : 
,
etc.
Acute : An acute angle is an angle less than
Example : 
,
etc.
Straight : A straight angle is .
Right: A right angle is .
Since the angle is more than but less than . So, it is an obtuse angle.
Answer:
40
Step-by-step explanation:
In the triangle, there is a 90 degree angle and Angle 1 (what we are looking for) and the other angle, lets call is Angle 2.
Lets find Angle 2 first.
First of all, the angle between angle 40 and 90 can be found easily.
That angle (lets call it "x) and 40 and 90 make a straight angle (180 degrees). So we can write:
40 + x + 90 = 180
Lets solve for "x":
40 + x + 90 = 180
130 + x = 180
x = 180 - 130
x = 50
Now, This angle (50) and Angle 2 are same [vertical angles]
So,
Angle 2 = 50
Now, there are 180 degrees in 3 angles in a triangle. So for the triangle shown, we cacn write:
90 + Angle 1 + Angle 2 = 180
90 + Angle 1 + 50 = 180
Angle 1 + 140 = 180
Angle 1 = 180 - 140
<u>Angle 1 = 40</u>
Answer:
Step-by-step explanation:
Multiply it all together
