smc-4552-10-sin

Trigonometry, SMB-032 MC

In which triangle is `sin theta = 4/7`?

A.		B.
C.		D.

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`=>D`

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`=>D`

Trigonometry, SMB-012

Find the value of `theta`, correct to one decimal place. (2 marks)

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`67.4^@`

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`sin theta`	`=12/13`
`theta`	`=sin^{-1}(12/13)`
	`=67.380…^@`
	`=67.4^@\ text{(to 1 d.p.)}`

Trigonometry, SMB-011

Find the value of `theta`, correct to the nearest minute. (2 marks)

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`60^@ 4^{′}`

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`sin theta`	`=13/15`
`theta`	`=sin^{-1}(13/15)`
	`=60.073…`
	`=60^@ 4^{′}`

Trigonometry, SMB-010

Find the value of `theta`, correct to the nearest minute. (2 marks)

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`38^@ 41^{′}`

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`sin theta`	`=10/16`
`theta`	`=sin^{-1}(5/8)`
	`=38.68…`
	`=38^@ 41^{′}`

Trigonometry, SMB-009

Use trigonometry to find the value of `x`, correct to 1 decimal place. (2 marks)

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`12.2`

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`sin 64^@`	`=11/x`
`x`	`=11/(sin 64^@)`
	`=12.2\ \ text{(to 1 d.p.)}`

Trigonometry, SMB-008

Use trigonometry to find the value of `x`, correct to 1 decimal place. (2 marks)

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`10.5`

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`sin 35^@`	`=6/x`
`x`	`=6/(sin 35^@)`
	`=10.5\ \ text{(to 1 d.p.)}`

Trigonometry, SMB-007

Find the value of `x`, correct to 2 decimal places. (2 marks)

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`16.17`

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`sin 72^@`	`=x/17`
`x`	`=17 xx sin 72^@`
	`=16.17\ \ text{(to 2 d.p.)}`

Trigonometry, SMB-006

Find the value of `x`, correct to 2 decimal places. (2 marks)

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`5.28`

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`sin 49^@`	`=x/7`
`x`	`=7 xx sin 49^@`
`x`	`=5.28\ \ text{(to 2 d.p.)}`

Trigonometry, SMB-005

Express `sin theta` as a fraction. (2 marks)

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`sin theta = 5/sqrt29`

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`text{By Pythagoras:}`

`x^2`	`=5^2 + 2^2`
`x^2`	`=29`
`x`	`=sqrt29\ \ (x>0)`

`:. sin theta = 5/sqrt29`

Trigonometry, SMB-004

Without the use of a calculator, express the following as a fraction

`sin 30^{@}` (1 mark)

--- 1 WORK AREA LINES (style=lined) ---
`sin 60^{@}` (2 marks)

--- 3 WORK AREA LINES (style=lined) ---

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`sin 30^{@} = 1/2`
`sin 60^{@} = sqrt3/2`

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i. `sin 30^{@} = text{opp}/text{hyp} = 1/2`

ii. `text{Let}\ \ x =\ text{unknown side}`

`text{By Pythagoras:}`

`2^2`	`=x^2 + 1^2`
`x^2`	`=4-1`
`x`	`=sqrt3\ \ (x>0)`

`sin 60^{@} = text{opp}/text{hyp} = sqrt3/2`

Trigonometry, SMB-003

Express the following as a fraction

`sin theta` (1 mark)

--- 1 WORK AREA LINES (style=lined) ---
`tan theta` (1 mark)

--- 1 WORK AREA LINES (style=lined) ---

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`sin theta = 7/25`
`tan theta = 7/24`

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i. `sin theta = text{opp}/text{hyp} = 7/25`

ii. `tan theta = text{opp}/text{adj} = 7/24`

Trigonometry, SMB-001

Express the following as a fraction

`cos theta` (1 mark)

--- 1 WORK AREA LINES (style=lined) ---
`sin theta` (1 mark)

--- 1 WORK AREA LINES (style=lined) ---

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`cos theta = 12/13`
`sin theta = 5/13`

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i. `cos theta = text{adj}/text{hyp} = 12/13`

ii. `sin theta = text{opp}/text{hyp} = 5/13`