The values of the trigonometry ratios are:
- cos α = - 5/13 and cot α = 5/12
- cot α = -5/12 and sec α = 13/5
<h3>How to solve the
trigonometry ratios?</h3>
<u>1: sin α = -12/13 and tan α > 0, find cos α and cot α</u>
Because tan α > 0, then it means that cos α and sin α are negative
So, we have:
sin²α + cos²α = 1
Substitute sin α = -12/13
(-12/13)² + cos²α = 1
This gives
cos²α = 1 - (-12/13)²
Evaluate the squares
cos²α = 1 - 144/169
Evaluate the difference
cos²α = 25/169
Take the square root of both sides
cos α = - 5/13
The cotangent ratio is represented as:
cot α = cos α/sin α
This gives
cot α = (-5/13)/(-12/13)
Evaluate
cot α = 5/12
Hence, cos α = - 5/13 and cot α = 5/12
<u>2: tan α = -12/5 for α in quadrant IV, find sec α and cot α</u>
Because α is in quadrant IV, then it means that sec α is positive
cot α = 1/tan α
This gives
cot α = 1/(-12/5)
Evaluate
cot α = -5/12
Also, we have:
sec²α = 1 + tan²α
Substitute tan α = -12/5
sec²α = 1 + (-12/5)²
Evaluate the squares
sec²α = 1 + 144/25
Evaluate the sum
sec²α = 169/25
Take the square root of both sides
sec α = 13/5
Hence, cot α = -5/12 and sec α = 13/5
Read more about trigonometry ratios at:
brainly.com/question/11967894
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Answer:
None
Step-by-step explanation:
By graphing out the both line segments through graphing software, segments AB and CD have no intersections on the co-ordinate plane.
I've attached a screenshot of what i graphed out.
He would need to play 12 average scoring games.
900 (goal) - 300 (has) = 600
and 600/50 is 12
hope this helps :)
Answer:
Step-by-step explanation:
Given that the bag contains black and red marbles.
Number of black marbles in the bag = 2
Number of red marbles in the bag = 3
Total number of marbles in the bag = Number of black marbles + Number of red marbles = 2 + 3 = 5
Let us have a look at the formula for probability of an event E, which can be observed as:
Now, the marble chosen at first is replaced.
Therefore, the count remains the same.
Now, the <em>required probability</em> can be found as:
Answer:
4x + 8x = 180
12x = 180
divide by 12 on both sides:
X = 15
4 x 15 = 60 degrees
8 x 15 = 120 degrees
