The value of$\cos \theta $ increases as $\theta $ increases. Enter 1 for true and 0 for false.
Answer
670.5k+ views
Hint: Look at the graph of cosine and check in the interval from 0 to 180. If the value of $\cos \theta $ increases as $\theta $ increases then the answer is 1 else it is 0.
Complete step-by-step answer:
For a right angled triangle, the ratio of the sides gives certain trigonometric functions.
$\cos \theta $is the ratio of the base and the perpendicular. So, $\cos \theta = \dfrac{b}{c}$.
Similarly, one can get the other trigonometric ratios as well by taking different sets of sides.
For different angles, one can plot the variation of this function with the varying angle$\theta $.
The graph of $\cos \theta $looks like:
The cosine function has the following properties:
It is a decreasing function from 0 to 180.
It is symmetric about the y axis.
It has $2\pi $ as its period.
In the interval 0 to 90 we can see that as the angle $\theta $ is increasing the function $\cos \theta $ will decrease from 1 to 0 and on further going from 90 to 180 the function takes values from 0 to -1. So, it is clear from the graph that the cosine function decreases in the interval 0 to 180.
So, the correct answer is a false so we enter 0.
Note: Since no interval was mentioned in the question the standard domain of 0 to 180 was taken. Otherwise, the graph is a sinusoidal curve and is either decreasing or increasing, according to the interval.
Complete step-by-step answer:
For a right angled triangle, the ratio of the sides gives certain trigonometric functions.
$\cos \theta $is the ratio of the base and the perpendicular. So, $\cos \theta = \dfrac{b}{c}$.
Similarly, one can get the other trigonometric ratios as well by taking different sets of sides.
For different angles, one can plot the variation of this function with the varying angle$\theta $.
The graph of $\cos \theta $looks like:
The cosine function has the following properties:
It is a decreasing function from 0 to 180.
It is symmetric about the y axis.
It has $2\pi $ as its period.
In the interval 0 to 90 we can see that as the angle $\theta $ is increasing the function $\cos \theta $ will decrease from 1 to 0 and on further going from 90 to 180 the function takes values from 0 to -1. So, it is clear from the graph that the cosine function decreases in the interval 0 to 180.
So, the correct answer is a false so we enter 0.
Note: Since no interval was mentioned in the question the standard domain of 0 to 180 was taken. Otherwise, the graph is a sinusoidal curve and is either decreasing or increasing, according to the interval.
Recently Updated Pages
Write structures of the following compounds i 2 Chloro3methylpentane class 11 chemistry CBSE

What is BLO What is the full form of BLO class 8 social science CBSE

Explain the Treaty of Vienna of 1815 class 10 social science CBSE

A Paragraph on Pollution in about 100-150 Words

XIX+XXX A 49 B 51 C 55 D 44 class 5 maths CBSE

If x a + bt + ct2 where x is in meters and t is in class 11 physics CBSE

Trending doubts
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Find the value of the expression given below sin 30circ class 11 maths CBSE

What do you mean by retardation What is its SI uni class 11 physics CBSE

Draw a diagram of nephron and explain its structur class 11 biology CBSE

10 examples of friction in our daily life

Difference between physical and chemical change class 11 chemistry CBSE

