$CATEGORY: Maths - TicTacLearn/8. Introduction to trignometry/8. Introduction to trignometry--Trigonometric Ratios

//Multiple Choice

In a right-angled triangle, the sine of an angle is defined as\: {
     ~ Adjacent side / Hypotenuse
     = Opposite side / Hypotenuse
     ~ Hypotenuse / Opposite side
     ~ Adjacent side / Opposite side
}

 The trigonometric ratio cosθ is the ratio of\: {
     = Adjacent side to the Hypotenuse
     ~ Opposite side to the Hypotenuse
     ~ Hypotenuse to the Adjacent side
     ~ Opposite side to the Adjacent side
}

 The value of tanθ is equal to\: {
     ~ sin⁡θ/cos⁡θ
     ~ cos⁡θ/sin⁡θ
     ~ 1/cot⁡θ
     = Both a and c
}

 The reciprocal of sin⁡θ is\: {
     ~ cos⁡θ
     ~ tan⁡θ
     = cosec⁡θ
     ~ sec⁡θ
}

 In a right-angled triangle, cot⁡θ is defined as\: {
     ~ Hypotenuse / Opposite side
     = Adjacent side / Opposite side
     ~ Opposite side / Adjacent side
     ~ Hypotenuse / Adjacent side
}

 The value of tan⁡45∘ is\: {
     = 1
     ~ 0
     ~ 1/2
     ~ None of these
}

 If tan⁡θ\=5/12, the hypotenuse of the right triangle is\: {
     ~ 12
     = 13
     ~ 5
     ~ 30
}

 The value of sin⁡60 is\: {
     ~ 1
     = √3/2
     ~ 0​
     ~ None of the above
}

//True or False

The value of tan⁡θ  is equal to sin⁡θ/cos⁡θ. {T}

sec⁡θ \= 1/cos⁡θ. {T}

sin⁡θ\=Adjacent side/Hypotenuse. {F}

The reciprocal of tan⁡θ is cot⁡θ. {T}

The value of sin⁡90∘ is 0. {F}

cot⁡θ  is the reciprocal of tan⁡θ. {T}

sin⁡2θ + cos2⁡θ \= 1  is true for all values of θ. {T}

The value of tan⁡0∘  is undefined. {F}

//Numericals



//Fill in the blanks

The trigonometric ratio sin⁡θ  is equal to ______. {
     = Opposite side / Hypotenuse
     ~ Adjacent side / Hypotenuse
     ~ Adjacent side / Opposite side
     ~ Hypotenuse / Opposite side
}

 sec⁡θ is the reciprocal of ______. {
     ~ sin⁡θ
     = cos⁡θ
     ~ tan⁡θ
     ~ cosec⁡θ
}

 The ratio of the opposite side to the adjacent side is called ______. {
     = tan⁡θ
     ~ sin⁡θ
     ~ cos⁡θ
     ~ sec⁡θ
}

 The value of cot⁡θ is equal to ______. {
     = 1/tan⁡θ
     ~ tan⁡θ
     ~ sin⁡θ/cos⁡θ
     ~ cos⁡θ
}

 The trigonometric identity sin⁡2θ + cos2⁡θ \= ______. {
     ~ 0
     = 1
     ~ tan⁡θ
     ~ cot⁡θ
}

 The value of sin⁡00 is ______. {
     ~ 1
     = 0
     ~ 1/2
     ~ 3/2
}

 The reciprocal of cos⁡θ is ______. {
     = sec⁡θ
     ~ cosec⁡θ
     ~ tan⁡θ
     ~ cot⁡θ
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=sin⁡θ -> Opposite/Hypotenuse
=cos⁡θ -> Adjacent/Hypotenuse
=tanθ -> Opposite/Adjacent
=secθ -> Hypotenuse/Adjacent
=cosecθ -> Hypotenuse/Opposite
}



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