STA100 Midterm Past Papers

Q1. Cos(-0)=?

1. Cos0
2. –cos0
3. Sin0
4. –Sin0

Q2. The smallest interval for which the fuction repeats itself is called:

1. Peroidic function
2. Period
3. Cosin function
4. Sine function

Q3. The range of cosin function is between:

1. -1 and 2
2. 1 and 2
3. -1 and 1
4. All of these

Q4. Sin0 is positive in ______quadrent and negative in _____quadrent:

1. 1st , 2nd
2. 3rd , 4th
3. 2nd , 3rd
4. 1st and 2nd, 3rd and 4th

Q5. Sin0=

1. PQ/OP
2. OP/PQ
3. P/Q d)O/P

Q6. Tan0 =

1. PQ/OQ
2. x/y
3. y/x
4. Both a and c

Q7. Tan0 is positive in ______quadrent:

1. 1st and 2nd b)1st and 3rd c)1st and 4th d)2nd and 3rd
2. Tan(180 -)Tan0 b) –tan0 c) Both d)None of these

Q9. The hight from the mean value of the function to its maximum or minimum value of a function is its:

1. Period b)Periodic function c)Range d)Amlitude

Q10. The range of y=arcsin x is :

1. [–pi and pi/4] b)[-pi and pi/2] c)[pi and pi/4] d)[Pi and pi/2]

Q11. The domain of y= arctan x is :

1. (- infinity and infinity) b)(Infinity and zero)
2. (–pi/2 and pi/2)
3. Both a and b

Q12. The inverse tangent function is defined by y=arctan x if and only if :

1. Tan x=x
2. Tan y=y c)Tan y=x d)Tan x=y 13)

The cosine function has period of

1. 180 b)360 c)240
2. 90

Q14. cosine function, has the range between:

1. -1 and 1.
2. 1and 3
3. 1and 2 d)-2and 1

Q15. For tangent function period is:

1. 90 b)80 c)180 d)260

Q16. Sin(theta -180)=?

1. Sin*
2. -sin*
3. Both d)Non An equation is not an identity is called a _____ equation:
4. Identical b)Non identical
5. Conditional d)Non conditional

Q17. In the reciprocal identity sec0=?

1. 1/cos0 b)1/sin0 c)1/tan0 d)1/csc0

Q18. In periodic properteis tan(0+pi)=

1. Sin 0 b)C0s 0 c)Tan 0 d)Sec0

Q19. In periodic properteis sec(0+2pi)=?

1. Csc0
2. Sec0
3. Cot0 d)Tan0

Q20. Tan 2 +1=?

1. Sec2
2. Sin 2
3. Cos2 d)Tan2

Q21. Tan(A-B)=

1. tanA – tanB/1+tanA tanB
2. tanA + tanB/1+tanA tanB
3. tanA + tanB/1-tanA tanB
4. tanA – tanB/1-tanA tanB
5. Varify that the following Equation is an identity:

Tan t-cot t/sin t cos t=sec2 t –csc2 t

Solution:

LHS= RHS

=tan t-cot t/sin t cos t=tan t/sin t cos t-cot t/sin t cos t

=tan t. 1/sin t cos t-cot t.1/sin t cos t

=sin t/cos t.1/sin t cos t-cos t /sin t.1/sin t cos t

=1/cos2 t-1/sin2 t

=sec2 t-csc 2 t

Q23. What is double angle formula?prove by sin, cos and tan0s?

=2tanA/1-tan2A

Prove =sin2A=sin(A+A)=sinA cosA+sinA cosA=2sinA cosA

=cos2A=cos(A+A)=cosA cosA-sinA sinA=cos2A –sin2A

=tan2A=tanA +tanA/1-tanA tanA=2tan A/1-tan2A

=2tan A/1-tan2A proved

24. To solve tan0 = k

Answer: ___find tan-1 (k)=0 ___use the peroidic property tan (180+-0)=tan(0) to get the other solution in the required interval.

Q25. Given that tan(63.43 degree)=2, solve tan0 = -2, giving all the roots in 0<0<360?

Answer: Ans : Find tan –1(-2) = -63.43 °, Note that -63.43 °is not in our range. Now use the periodic property tan(-63.43 °) = tan(-63.43 ° - 180 °) to get 116.56. Now use the periodic property tan(116.56 tan(116.56 ° + 180 °) to get 296.56 °. The solutions are is 116.6 º and 296.6

Q26. what is double angale formula?

o Double Angle Formulas:

▪sin2A=sin(A+A)=sinAcosA+sinAcosA = 2sinAcosA ▪22cos2A=cos(A+A)=cosAcosA-sinAsinA = cosA-sinA ▪2tanA+tanA2tanAtan2A==1-tanAtanA1-tanA

Q27. What is sum of difference formula?

o Sum and Difference Formulas:

cos(A-B) = cosAcosB + sinAsinB cos(A+B) = cosAcosB - sinAsinB

sin(A+B) = sinAcosB + cosAsinB sin(A-B) = sinAcosB – cosAsinB

▪tantantan()1tantanABABAB tantantan()1tantanABABAB

Q28. what are Periodic Properties ?

Q29. What are Pythagorean Identities ?

Answer: sin2(theta)+cos2(theta)=1

Q30. define conditional equation?

An equation that is not an identity is called a conditional equation.

Q31. Define an amplitute?

Definition: The Amplitude of a function is the height from the mean (or the rest) value of the function to its maximum or minimum value.

Q32. Difference between periodic function & period?

Definition: The functions with the property that they keep repeating themselves are called periodic functions. The smallest interval for which the function repeats itself is called its period.